Q1. The probability of getting a head when a fair coin is tossed is:

Difficulty: Easy · Topic: Classical Probability

Solution

Fair coin: P(H) = 1/2.

Q2. Probability of an impossible event is:

Difficulty: Easy · Topic: Impossible and Sure Events

Solution

An impossible event cannot occur. P = 0.

Q3. A bag contains 2 red balls and 10 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 2/10
B) 12/2
C) 2/12
D) 10/12

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 2 + 10\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{2}{2+10} = 2/12\)

Q4. A bag contains 13 red balls and 13 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 13/13
B) 26/13
C) 13/26
D) N/A (1)

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 13 + 13\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{13}{13+13} = 13/26\)

Q5. A bag contains 8 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 22/8
B) 14/22
C) 8/14
D) 8/22

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+14} = 8/22\)

Q6. A bag contains 9 red balls and 12 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 12/21
B) 21/9
C) 9/21
D) 9/12

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 9 + 12\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{9}{9+12} = 9/21\)

Q7. A bag contains 2 red balls and 13 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 2/15
B) 2/13
C) 15/2
D) 13/15

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 2 + 13\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{2}{2+13} = 2/15\)

Q8. A bag contains 11 red balls and 7 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 11/18
B) 11/7
C) 7/18
D) 18/11

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 11 + 7\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{11}{11+7} = 11/18\)

Q9. A bag contains 10 red balls and 11 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 11/21
B) 21/10
C) 10/11
D) 10/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 11\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+11} = 10/21\)

Q10. A bag contains 3 red balls and 9 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 3/12
B) 12/3
C) 9/12
D) 3/9

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 3 + 9\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{3}{3+9} = 3/12\)

Q11. A bag contains 8 red balls and 3 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 11/8
B) 3/11
C) 8/11
D) 8/3

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 3\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+3} = 8/11\)

Q12. A bag contains 14 red balls and 4 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 14/4
B) 4/18
C) 14/18
D) 18/14

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 14 + 4\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{14}{14+4} = 14/18\)

Q13. A bag contains 11 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 11/14
B) 11/25
C) 25/11
D) 14/25

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 11 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{11}{11+14} = 11/25\)

Q14. A bag contains 11 red balls and 13 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 24/11
B) 11/24
C) 13/24
D) 11/13

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 11 + 13\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{11}{11+13} = 11/24\)

Q15. A bag contains 10 red balls and 15 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/25
B) 25/10
C) 10/25
D) 10/15

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 15\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+15} = 10/25\)

Q16. A bag contains 7 red balls and 4 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 7/4
B) 11/7
C) 7/11
D) 4/11

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 7 + 4\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{7}{7+4} = 7/11\)

Q17. A bag contains 14 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) N/A (1)
B) 14/14
C) 28/14
D) 14/28

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 14 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{14}{14+14} = 14/28\)

Q18. A bag contains 14 red balls and 10 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 14/24
B) 14/10
C) 10/24
D) 24/14

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 14 + 10\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{14}{14+10} = 14/24\)

Q19. A bag contains 10 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/10
B) 10/5
C) 5/15
D) 10/15

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+5} = 10/15\)

Q20. A bag contains 10 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 10/14
B) 24/10
C) 10/24
D) 14/24

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+14} = 10/24\)

Q21. A bag contains 10 red balls and 12 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 10/22
B) 10/12
C) 22/10
D) 12/22

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 12\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+12} = 10/22\)

Q22. A bag contains 5 red balls and 13 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 18/5
B) 5/18
C) 5/13
D) 13/18

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 5 + 13\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{5}{5+13} = 5/18\)

Q23. A bag contains 5 red balls and 11 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 5/16
B) 16/5
C) 5/11
D) 11/16

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 5 + 11\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{5}{5+11} = 5/16\)

Q24. A bag contains 3 red balls and 10 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 3/10
B) 3/13
C) 10/13
D) 13/3

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 3 + 10\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{3}{3+10} = 3/13\)

Q25. A bag contains 14 red balls and 2 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 2/16
B) 14/16
C) 16/14
D) 14/2

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 14 + 2\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{14}{14+2} = 14/16\)

Q26. A bag contains 4 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/4
B) 5/9
C) 4/9
D) 4/5

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 4 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{4}{4+5} = 4/9\)

Q27. A bag contains 11 red balls and 8 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 11/19
B) 19/11
C) 11/8
D) 8/19

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 11 + 8\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{11}{11+8} = 11/19\)

Q28. A bag contains 15 red balls and 6 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 6/21
B) 15/6
C) 21/15
D) 15/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 6\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+6} = 15/21\)

Q29. A bag contains 13 red balls and 3 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 16/13
B) 3/16
C) 13/16
D) 13/3

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 13 + 3\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{13}{13+3} = 13/16\)

Q30. A bag contains 7 red balls and 3 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 3/10
B) 7/3
C) 10/7
D) 7/10

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 7 + 3\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{7}{7+3} = 7/10\)

Q31. A bag contains 13 red balls and 6 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 13/19
B) 19/13
C) 6/19
D) 13/6

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 13 + 6\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{13}{13+6} = 13/19\)

Q32. A bag contains 8 red balls and 13 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/13
B) 8/21
C) 13/21
D) 21/8

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 13\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+13} = 8/21\)

Q33. A bag contains 5 red balls and 4 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 4/9
B) 5/4
C) 5/9
D) 9/5

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 5 + 4\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{5}{5+4} = 5/9\)

Q34. A bag contains 7 red balls and 12 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 12/19
B) 19/7
C) 7/12
D) 7/19

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 7 + 12\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{7}{7+12} = 7/19\)

Q35. A bag contains 12 red balls and 9 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/21
B) 21/12
C) 12/9
D) 12/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 12 + 9\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{12}{12+9} = 12/21\)

Q36. A bag contains 6 red balls and 2 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/6
B) 6/8
C) 2/8
D) 6/2

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 6 + 2\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{6}{6+2} = 6/8\)

Q37. A bag contains 15 red balls and 8 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/8
B) 15/23
C) 23/15
D) 8/23

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 8\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+8} = 15/23\)

Q38. A bag contains 15 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 20/15
B) 15/5
C) 15/20
D) 5/20

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+5} = 15/20\)

Q39. A bag contains 2 red balls and 6 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/2
B) 2/6
C) 6/8
D) 2/8

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 2 + 6\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{2}{2+6} = 2/8\)

Q40. A bag contains 9 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/14
B) 9/23
C) 14/23
D) 23/9

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 9 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{9}{9+14} = 9/23\)

Q41. A bag contains 13 red balls and 8 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 13/21
B) 13/8
C) 21/13
D) 8/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 13 + 8\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{13}{13+8} = 13/21\)

Q42. A bag contains 4 red balls and 6 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 4/6
B) 6/10
C) 4/10
D) 10/4

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 4 + 6\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{4}{4+6} = 4/10\)

Q43. A bag contains 15 red balls and 11 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/26
B) 11/26
C) 15/11
D) 26/15

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 11\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+11} = 15/26\)

Q44. A bag contains 10 red balls and 3 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 13/10
B) 3/13
C) 10/3
D) 10/13

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 10 + 3\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{10}{10+3} = 10/13\)

Q45. A bag contains 15 red balls and 12 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/27
B) 27/15
C) 12/27
D) 15/12

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 12\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+12} = 15/27\)

Q46. A bag contains 8 red balls and 12 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/20
B) 8/12
C) 12/20
D) 20/8

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 12\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+12} = 8/20\)

Q47. A bag contains 5 red balls and 15 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 5/15
B) 15/20
C) 20/5
D) 5/20

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 5 + 15\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{5}{5+15} = 5/20\)

Q48. A bag contains 4 red balls and 11 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 4/11
B) 4/15
C) 11/15
D) 15/4

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 4 + 11\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{4}{4+11} = 4/15\)

Q49. A bag contains 9 red balls and 15 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/15
B) 9/24
C) 15/24
D) 24/9

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 9 + 15\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{9}{9+15} = 9/24\)

Q50. A bag contains 8 red balls and 8 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) N/A (1)
B) 8/8
C) 16/8
D) 8/16

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 8\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+8} = 8/16\)

Q51. A bag contains 5 red balls and 8 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 5/13
B) 13/5
C) 5/8
D) 8/13

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 5 + 8\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{5}{5+8} = 5/13\)

Q52. A bag contains 7 red balls and 14 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 21/7
B) 7/21
C) 7/14
D) 14/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 7 + 14\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{7}{7+14} = 7/21\)

Q53. A bag contains 8 red balls and 2 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 10/8
B) 2/10
C) 8/2
D) 8/10

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 2\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+2} = 8/10\)

Q54. A bag contains 3 red balls and 2 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 2/5
B) 3/2
C) 5/3
D) 3/5

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 3 + 2\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{3}{3+2} = 3/5\)

Q55. A bag contains 6 red balls and 10 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 6/10
B) 10/16
C) 16/6
D) 6/16

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 6 + 10\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{6}{6+10} = 6/16\)

Q56. A bag contains 8 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/5
B) 8/13
C) 13/8
D) 5/13

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+5} = 8/13\)

Q57. A bag contains 6 red balls and 11 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 6/11
B) 17/6
C) 6/17
D) 11/17

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 6 + 11\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{6}{6+11} = 6/17\)

Q58. A bag contains 9 red balls and 9 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/9
B) 18/9
C) 9/18
D) N/A (1)

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 9 + 9\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{9}{9+9} = 9/18\)

Q59. A bag contains 13 red balls and 9 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 22/13
B) 13/9
C) 9/22
D) 13/22

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 13 + 9\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{13}{13+9} = 13/22\)

Q60. A bag contains 4 red balls and 4 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 4/8
B) N/A (1)
C) 4/4
D) 8/4

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 4 + 4\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{4}{4+4} = 4/8\)

Q61. A bag contains 3 red balls and 7 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 3/7
B) 10/3
C) 3/10
D) 7/10

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 3 + 7\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{3}{3+7} = 3/10\)

Q62. A bag contains 8 red balls and 15 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 8/15
B) 23/8
C) 8/23
D) 15/23

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 8 + 15\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{8}{8+15} = 8/23\)

Q63. A bag contains 6 red balls and 15 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 6/15
B) 21/6
C) 15/21
D) 6/21

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 6 + 15\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{6}{6+15} = 6/21\)

Q64. A bag contains 15 red balls and 7 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 7/22
B) 15/7
C) 15/22
D) 22/15

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 7\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+7} = 15/22\)

Q65. A bag contains 14 red balls and 9 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 23/14
B) 14/23
C) 14/9
D) 9/23

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 14 + 9\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{14}{14+9} = 14/23\)

Q66. A bag contains 2 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 5/7
B) 2/7
C) 2/5
D) 7/2

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 2 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{2}{2+5} = 2/7\)

Q67. A bag contains 15 red balls and 4 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 15/19
B) 19/15
C) 15/4
D) 4/19

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 15 + 4\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{15}{15+4} = 15/19\)

Q68. A bag contains 9 red balls and 5 blue balls. One ball is drawn at random. What is the probability of getting a red ball?

A) 9/14
B) 9/5
C) 14/9
D) 5/14

Difficulty: Easy · Topic: Probability from a bag of balls

Solution

Total balls \(= 9 + 5\)

\(P(\text{red}) = \frac{\text{red balls}}{\text{total balls}} = \frac{9}{9+5} = 9/14\)

Q69. A die is thrown once. Find the probability of getting a number greater than 4.

Difficulty: Easy-Medium · Topic: Classical Probability

Solution

Favourable: {5,6} = 2 outcomes. Total = 6. P = 2/6 = 1/3.

Q70. Two coins are tossed simultaneously. Find the probability of getting at least one head.

Difficulty: Easy-Medium · Topic: Classical Probability

Solution

Sample space: {HH, HT, TH, TT}. At least one head: {HH, HT, TH} = 3. P = 3/4.

Q71. A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting a queen.

Difficulty: Easy-Medium · Topic: Classical Probability

Solution

Queens = 4. P = 4/52 = 1/13.

Q72. If P(E) = 0.05, what is P(not E)?

Difficulty: Easy-Medium · Topic: Complementary Events

Solution

P(not E) = 1 − 0.05 = 0.95.

Q73. A jar contains 24 marbles: 6 white, 9 green, and the rest blue. A marble is drawn randomly. Find P(blue).

Difficulty: Easy-Medium · Topic: Classical Probability

Solution

Blue = 24−6−9 = 9. P = 9/24 = 3/8.

Q74. A bag contains 2 red, 10 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 2/21
B) 10/21
C) 11/11
D) 11/21

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+10+9. Non-green = 2+9.

\(P(\text{not green}) = \frac{2+9}{2+10+9} = 11/21\)

Q75. A bag contains 8 red, 6 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 6/22
B) 16/22
C) 8/22
D) 16/16

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+6+8. Non-green = 8+8.

\(P(\text{not green}) = \frac{8+8}{8+6+8} = 16/22\)

Q76. A bag contains 5 red, 8 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 5/15
B) 8/15
C) 7/7
D) 7/15

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+8+2. Non-green = 5+2.

\(P(\text{not green}) = \frac{5+2}{5+8+2} = 7/15\)

Q77. A bag contains 7 red, 5 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 7/16
B) 5/16
C) 11/16
D) 11/11

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+5+4. Non-green = 7+4.

\(P(\text{not green}) = \frac{7+4}{7+5+4} = 11/16\)

Q78. A bag contains 10 red, 3 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 10/16
B) 13/13
C) 13/16
D) 3/16

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+3+3. Non-green = 10+3.

\(P(\text{not green}) = \frac{10+3}{10+3+3} = 13/16\)

Q79. A bag contains 8 red, 4 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 16/16
B) 16/20
C) 8/20
D) 4/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+4+8. Non-green = 8+8.

\(P(\text{not green}) = \frac{8+8}{8+4+8} = 16/20\)

Q80. A bag contains 8 red, 3 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 8/20
B) 17/20
C) 3/20
D) 17/17

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+3+9. Non-green = 8+9.

\(P(\text{not green}) = \frac{8+9}{8+3+9} = 17/20\)

Q81. A bag contains 4 red, 8 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 8/21
B) 13/13
C) 13/21
D) 4/21

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+8+9. Non-green = 4+9.

\(P(\text{not green}) = \frac{4+9}{4+8+9} = 13/21\)

Q82. A bag contains 3 red, 7 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 13/20
B) 13/13
C) 7/20
D) 3/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+7+10. Non-green = 3+10.

\(P(\text{not green}) = \frac{3+10}{3+7+10} = 13/20\)

Q83. A bag contains 7 red, 8 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 10/10
B) 10/18
C) 7/18
D) 8/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+8+3. Non-green = 7+3.

\(P(\text{not green}) = \frac{7+3}{7+8+3} = 10/18\)

Q84. A bag contains 5 red, 3 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 15/15
B) 3/18
C) 15/18
D) 5/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+3+10. Non-green = 5+10.

\(P(\text{not green}) = \frac{5+10}{5+3+10} = 15/18\)

Q85. A bag contains 3 red, 8 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 9/9
B) 8/17
C) 9/17
D) 3/17

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+8+6. Non-green = 3+6.

\(P(\text{not green}) = \frac{3+6}{3+8+6} = 9/17\)

Q86. A bag contains 7 red, 9 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 7/25
B) 16/16
C) 16/25
D) 9/25

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+9+9. Non-green = 7+9.

\(P(\text{not green}) = \frac{7+9}{7+9+9} = 16/25\)

Q87. A bag contains 4 red, 3 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 4/17
B) 14/17
C) 14/14
D) 3/17

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+3+10. Non-green = 4+10.

\(P(\text{not green}) = \frac{4+10}{4+3+10} = 14/17\)

Q88. A bag contains 3 red, 8 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 13/21
B) 3/21
C) 13/13
D) 8/21

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+8+10. Non-green = 3+10.

\(P(\text{not green}) = \frac{3+10}{3+8+10} = 13/21\)

Q89. A bag contains 5 red, 2 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 5/13
B) 11/11
C) 2/13
D) 11/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+2+6. Non-green = 5+6.

\(P(\text{not green}) = \frac{5+6}{5+2+6} = 11/13\)

Q90. A bag contains 9 red, 2 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 2/13
B) 11/13
C) 11/11
D) 9/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+2+2. Non-green = 9+2.

\(P(\text{not green}) = \frac{9+2}{9+2+2} = 11/13\)

Q91. A bag contains 2 red, 8 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 7/7
B) 8/15
C) 7/15
D) 2/15

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+8+5. Non-green = 2+5.

\(P(\text{not green}) = \frac{2+5}{2+8+5} = 7/15\)

Q92. A bag contains 7 red, 9 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 9/26
B) 17/17
C) 17/26
D) 7/26

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+9+10. Non-green = 7+10.

\(P(\text{not green}) = \frac{7+10}{7+9+10} = 17/26\)

Q93. A bag contains 2 red, 3 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 2/14
B) 11/11
C) 11/14
D) 3/14

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+3+9. Non-green = 2+9.

\(P(\text{not green}) = \frac{2+9}{2+3+9} = 11/14\)

Q94. A bag contains 10 red, 2 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 2/18
B) 16/18
C) 16/16
D) 10/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+2+6. Non-green = 10+6.

\(P(\text{not green}) = \frac{10+6}{10+2+6} = 16/18\)

Q95. A bag contains 10 red, 4 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 10/17
B) 13/13
C) 13/17
D) 4/17

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+4+3. Non-green = 10+3.

\(P(\text{not green}) = \frac{10+3}{10+4+3} = 13/17\)

Q96. A bag contains 4 red, 5 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 5/12
B) 4/12
C) 7/12
D) 7/7

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+5+3. Non-green = 4+3.

\(P(\text{not green}) = \frac{4+3}{4+5+3} = 7/12\)

Q97. A bag contains 2 red, 6 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 6/12
B) N/A (1)
C) 6/6
D) 2/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+6+4. Non-green = 2+4.

\(P(\text{not green}) = \frac{2+4}{2+6+4} = 6/12\)

Q98. A bag contains 9 red, 8 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 9/26
B) 18/26
C) 18/18
D) 8/26

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+8+9. Non-green = 9+9.

\(P(\text{not green}) = \frac{9+9}{9+8+9} = 18/26\)

Q99. A bag contains 3 red, 9 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 6/6
B) 6/15
C) 9/15
D) 3/15

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+9+3. Non-green = 3+3.

\(P(\text{not green}) = \frac{3+3}{3+9+3} = 6/15\)

Q100. A bag contains 7 red, 10 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 10/10
B) 7/20
C) N/A (1)
D) 10/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+10+3. Non-green = 7+3.

\(P(\text{not green}) = \frac{7+3}{7+10+3} = 10/20\)

Q101. A bag contains 8 red, 10 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 18/28
B) 10/28
C) 8/28
D) 18/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+10+10. Non-green = 8+10.

\(P(\text{not green}) = \frac{8+10}{8+10+10} = 18/28\)

Q102. A bag contains 4 red, 6 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 8/14
B) 6/14
C) 4/14
D) 8/8

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+6+4. Non-green = 4+4.

\(P(\text{not green}) = \frac{4+4}{4+6+4} = 8/14\)

Q103. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a face card.

A) 40/52
B) 13/52
C) 12/13
D) 12/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of face cards = 12

P(face card) = 12/52

Q104. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a queen.

A) 4/52
B) 4/13
C) 48/52
D) 5/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of queens = 4

P(queen) = 4/52

Q105. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a red queen.

A) 2/13
B) 50/52
C) 2/52
D) 3/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of red queens = 2

P(red queen) = 2/52

Q106. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a spade.

A) 39/52
B) 14/52
C) 13/52
D) 13/13

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of spades = 13

P(spade) = 13/52

Q107. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a heart.

A) 13/52
B) 13/13
C) 14/52
D) 39/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of hearts = 13

P(heart) = 13/52

Q108. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a jack.

A) 48/52
B) 4/52
C) 5/52
D) 4/13

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of jacks = 4

P(jack) = 4/52

Q109. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a ace.

A) 5/52
B) 48/52
C) 4/52
D) 4/13

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of aces = 4

P(ace) = 4/52

Q110. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a red card.

A) N/A (1)
B) 27/52
C) 26/52
D) 26/13

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of red cards = 26

P(red card) = 26/52

Q111. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a black king.

A) 3/52
B) 2/52
C) 50/52
D) 2/13

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of black kings = 2

P(black king) = 2/52

Q112. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a diamond.

A) 13/52
B) 14/52
C) 13/13
D) 39/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of diamonds = 13

P(diamond) = 13/52

Q113. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king.

A) 4/13
B) 48/52
C) 4/52
D) 5/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of kings = 4

P(king) = 4/52

Q114. A bag contains 5 red, 5 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) N/A (1)
B) 5/12
C) 7/7
D) 7/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+5+2. Non-green = 5+2.

\(P(\text{not green}) = \frac{5+2}{5+5+2} = 7/12\)

Q115. A bag contains 2 red, 2 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 8/8
B) N/A (1)
C) 8/10
D) 2/10

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+2+6. Non-green = 2+6.

\(P(\text{not green}) = \frac{2+6}{2+2+6} = 8/10\)

Q116. A bag contains 3 red, 7 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 3/19
B) 12/12
C) 7/19
D) 12/19

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+7+9. Non-green = 3+9.

\(P(\text{not green}) = \frac{3+9}{3+7+9} = 12/19\)

Q117. A bag contains 4 red, 3 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 3/10
B) 4/10
C) 7/10
D) 7/7

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+3+3. Non-green = 4+3.

\(P(\text{not green}) = \frac{4+3}{4+3+3} = 7/10\)

Q118. A bag contains 6 red, 7 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) 7/20
B) 6/20
C) 13/13
D) 13/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+7+7. Non-green = 6+7.

\(P(\text{not green}) = \frac{6+7}{6+7+7} = 13/20\)

Q119. A bag contains 4 red, 2 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 7/9
B) 7/7
C) 2/9
D) 4/9

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+2+3. Non-green = 4+3.

\(P(\text{not green}) = \frac{4+3}{4+2+3} = 7/9\)

Q120. A bag contains 9 red, 2 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 2/14
B) 9/14
C) 12/12
D) 12/14

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+2+3. Non-green = 9+3.

\(P(\text{not green}) = \frac{9+3}{9+2+3} = 12/14\)

Q121. A bag contains 4 red, 4 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 8/8
B) N/A (1)
C) 8/12
D) 4/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+4+4. Non-green = 4+4.

\(P(\text{not green}) = \frac{4+4}{4+4+4} = 8/12\)

Q122. A bag contains 4 red, 4 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 4/14
B) 10/14
C) N/A (1)
D) 10/10

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+4+6. Non-green = 4+6.

\(P(\text{not green}) = \frac{4+6}{4+4+6} = 10/14\)

Q123. A bag contains 9 red, 6 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 19/19
B) 9/25
C) 6/25
D) 19/25

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+6+10. Non-green = 9+10.

\(P(\text{not green}) = \frac{9+10}{9+6+10} = 19/25\)

Q124. A bag contains 9 red, 6 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 18/24
B) 6/24
C) 9/24
D) 18/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+6+9. Non-green = 9+9.

\(P(\text{not green}) = \frac{9+9}{9+6+9} = 18/24\)

Q125. A bag contains 6 red, 4 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 12/16
B) 12/12
C) 4/16
D) 6/16

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+4+6. Non-green = 6+6.

\(P(\text{not green}) = \frac{6+6}{6+4+6} = 12/16\)

Q126. A bag contains 6 red, 3 green, and 10 blue balls. What is the probability of NOT drawing a green ball?

A) 16/19
B) 16/16
C) 6/19
D) 3/19

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+3+10. Non-green = 6+10.

\(P(\text{not green}) = \frac{6+10}{6+3+10} = 16/19\)

Q127. A bag contains 4 red, 3 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 3/9
B) 6/6
C) 6/9
D) 4/9

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+3+2. Non-green = 4+2.

\(P(\text{not green}) = \frac{4+2}{4+3+2} = 6/9\)

Q128. A bag contains 4 red, 10 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 9/19
B) 10/19
C) 4/19
D) 9/9

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+10+5. Non-green = 4+5.

\(P(\text{not green}) = \frac{4+5}{4+10+5} = 9/19\)

Q129. A bag contains 7 red, 10 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 13/23
B) 10/23
C) 13/13
D) 7/23

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+10+6. Non-green = 7+6.

\(P(\text{not green}) = \frac{7+6}{7+10+6} = 13/23\)

Q130. A bag contains 9 red, 7 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 9/25
B) 18/25
C) 7/25
D) 18/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 9+7+9. Non-green = 9+9.

\(P(\text{not green}) = \frac{9+9}{9+7+9} = 18/25\)

Q131. A bag contains 3 red, 2 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) 10/12
B) 10/10
C) 3/12
D) 2/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+2+7. Non-green = 3+7.

\(P(\text{not green}) = \frac{3+7}{3+2+7} = 10/12\)

Q132. A bag contains 2 red, 2 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) 9/9
B) 2/11
C) 9/11
D) N/A (1)

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+2+7. Non-green = 2+7.

\(P(\text{not green}) = \frac{2+7}{2+2+7} = 9/11\)

Q133. A bag contains 2 red, 9 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 9/13
B) 4/13
C) 2/13
D) 4/4

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+9+2. Non-green = 2+2.

\(P(\text{not green}) = \frac{2+2}{2+9+2} = 4/13\)

Q134. A bag contains 4 red, 8 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 4/14
B) 8/14
C) 6/14
D) 6/6

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+8+2. Non-green = 4+2.

\(P(\text{not green}) = \frac{4+2}{4+8+2} = 6/14\)

Q135. A bag contains 4 red, 3 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 9/9
B) 4/12
C) 9/12
D) 3/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+3+5. Non-green = 4+5.

\(P(\text{not green}) = \frac{4+5}{4+3+5} = 9/12\)

Q136. A bag contains 4 red, 8 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 8/8
B) 8/16
C) 4/16
D) N/A (1)

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+8+4. Non-green = 4+4.

\(P(\text{not green}) = \frac{4+4}{4+8+4} = 8/16\)

Q137. A bag contains 2 red, 2 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 11/13
B) 11/11
C) N/A (1)
D) 2/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+2+9. Non-green = 2+9.

\(P(\text{not green}) = \frac{2+9}{2+2+9} = 11/13\)

Q138. A bag contains 5 red, 3 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 9/9
B) 5/12
C) 9/12
D) 3/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+3+4. Non-green = 5+4.

\(P(\text{not green}) = \frac{5+4}{5+3+4} = 9/12\)

Q139. A bag contains 3 red, 6 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 6/6
B) 6/12
C) N/A (1)
D) 3/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+6+3. Non-green = 3+3.

\(P(\text{not green}) = \frac{3+3}{3+6+3} = 6/12\)

Q140. A bag contains 6 red, 6 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 6/17
B) 11/17
C) N/A (1)
D) 11/11

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+6+5. Non-green = 6+5.

\(P(\text{not green}) = \frac{6+5}{6+6+5} = 11/17\)

Q141. A bag contains 8 red, 2 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 16/18
B) 8/18
C) 16/16
D) 2/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+2+8. Non-green = 8+8.

\(P(\text{not green}) = \frac{8+8}{8+2+8} = 16/18\)

Q142. A bag contains 8 red, 4 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 4/14
B) 10/10
C) 8/14
D) 10/14

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+4+2. Non-green = 8+2.

\(P(\text{not green}) = \frac{8+2}{8+4+2} = 10/14\)

Q143. A bag contains 2 red, 2 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) N/A (1)
B) 10/10
C) 2/12
D) 10/12

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+2+8. Non-green = 2+8.

\(P(\text{not green}) = \frac{2+8}{2+2+8} = 10/12\)

Q144. A bag contains 2 red, 6 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 2/13
B) 7/7
C) 7/13
D) 6/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+6+5. Non-green = 2+5.

\(P(\text{not green}) = \frac{2+5}{2+6+5} = 7/13\)

Q145. A bag contains 8 red, 10 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 10/10
B) 8/20
C) N/A (1)
D) 10/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 8+10+2. Non-green = 8+2.

\(P(\text{not green}) = \frac{8+2}{8+10+2} = 10/20\)

Q146. A bag contains 6 red, 4 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 6/13
B) 9/9
C) 9/13
D) 4/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+4+3. Non-green = 6+3.

\(P(\text{not green}) = \frac{6+3}{6+4+3} = 9/13\)

Q147. A bag contains 10 red, 7 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 18/18
B) 18/25
C) 7/25
D) 10/25

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+7+8. Non-green = 10+8.

\(P(\text{not green}) = \frac{10+8}{10+7+8} = 18/25\)

Q148. A bag contains 2 red, 4 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 2/8
B) 4/4
C) N/A (1)
D) 4/8

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+4+2. Non-green = 2+2.

\(P(\text{not green}) = \frac{2+2}{2+4+2} = 4/8\)

Q149. A bag contains 4 red, 7 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) 11/11
B) 7/18
C) 4/18
D) 11/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+7+7. Non-green = 4+7.

\(P(\text{not green}) = \frac{4+7}{4+7+7} = 11/18\)

Q150. A bag contains 10 red, 6 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) 10/21
B) 6/21
C) 15/21
D) 15/15

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+6+5. Non-green = 10+5.

\(P(\text{not green}) = \frac{10+5}{10+6+5} = 15/21\)

Q151. A bag contains 6 red, 5 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 14/14
B) 5/19
C) 6/19
D) 14/19

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+5+8. Non-green = 6+8.

\(P(\text{not green}) = \frac{6+8}{6+5+8} = 14/19\)

Q152. A bag contains 5 red, 2 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 2/10
B) 8/8
C) 5/10
D) 8/10

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+2+3. Non-green = 5+3.

\(P(\text{not green}) = \frac{5+3}{5+2+3} = 8/10\)

Q153. A bag contains 10 red, 4 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 4/23
B) 10/23
C) 19/23
D) 19/19

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+4+9. Non-green = 10+9.

\(P(\text{not green}) = \frac{10+9}{10+4+9} = 19/23\)

Q154. A bag contains 6 red, 7 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 12/12
B) 6/19
C) 12/19
D) 7/19

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+7+6. Non-green = 6+6.

\(P(\text{not green}) = \frac{6+6}{6+7+6} = 12/19\)

Q155. A bag contains 7 red, 4 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) 7/18
B) 14/14
C) 14/18
D) 4/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 7+4+7. Non-green = 7+7.

\(P(\text{not green}) = \frac{7+7}{7+4+7} = 14/18\)

Q156. A bag contains 3 red, 2 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 3/9
B) 7/9
C) 7/7
D) 2/9

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+2+4. Non-green = 3+4.

\(P(\text{not green}) = \frac{3+4}{3+2+4} = 7/9\)

Q157. A bag contains 4 red, 7 green, and 2 blue balls. What is the probability of NOT drawing a green ball?

A) 7/13
B) 4/13
C) 6/6
D) 6/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+7+2. Non-green = 4+2.

\(P(\text{not green}) = \frac{4+2}{4+7+2} = 6/13\)

Q158. A bag contains 6 red, 5 green, and 4 blue balls. What is the probability of NOT drawing a green ball?

A) 10/10
B) 10/15
C) 6/15
D) 5/15

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+5+4. Non-green = 6+4.

\(P(\text{not green}) = \frac{6+4}{6+5+4} = 10/15\)

Q159. A bag contains 5 red, 2 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 5/16
B) 2/16
C) 14/14
D) 14/16

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+2+9. Non-green = 5+9.

\(P(\text{not green}) = \frac{5+9}{5+2+9} = 14/16\)

Q160. A bag contains 2 red, 3 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 8/8
B) 2/11
C) 3/11
D) 8/11

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+3+6. Non-green = 2+6.

\(P(\text{not green}) = \frac{2+6}{2+3+6} = 8/11\)

Q161. A bag contains 3 red, 3 green, and 5 blue balls. What is the probability of NOT drawing a green ball?

A) N/A (1)
B) 8/8
C) 3/11
D) 8/11

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 3+3+5. Non-green = 3+5.

\(P(\text{not green}) = \frac{3+5}{3+3+5} = 8/11\)

Q162. A bag contains 6 red, 2 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 2/11
B) 9/11
C) 9/9
D) 6/11

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+2+3. Non-green = 6+3.

\(P(\text{not green}) = \frac{6+3}{6+2+3} = 9/11\)

Q163. A bag contains 6 red, 9 green, and 8 blue balls. What is the probability of NOT drawing a green ball?

A) 14/23
B) 6/23
C) 14/14
D) 9/23

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 6+9+8. Non-green = 6+8.

\(P(\text{not green}) = \frac{6+8}{6+9+8} = 14/23\)

Q164. A bag contains 2 red, 5 green, and 6 blue balls. What is the probability of NOT drawing a green ball?

A) 5/13
B) 8/13
C) 8/8
D) 2/13

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+5+6. Non-green = 2+6.

\(P(\text{not green}) = \frac{2+6}{2+5+6} = 8/13\)

Q165. A bag contains 2 red, 9 green, and 7 blue balls. What is the probability of NOT drawing a green ball?

A) N/A (1)
B) 2/18
C) 9/9
D) 9/18

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+9+7. Non-green = 2+7.

\(P(\text{not green}) = \frac{2+7}{2+9+7} = 9/18\)

Q166. A bag contains 2 red, 10 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 5/15
B) 2/15
C) 10/15
D) 5/5

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 2+10+3. Non-green = 2+3.

\(P(\text{not green}) = \frac{2+3}{2+10+3} = 5/15\)

Q167. A bag contains 5 red, 7 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 7/21
B) 14/21
C) 5/21
D) 14/14

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 5+7+9. Non-green = 5+9.

\(P(\text{not green}) = \frac{5+9}{5+7+9} = 14/21\)

Q168. A bag contains 10 red, 7 green, and 3 blue balls. What is the probability of NOT drawing a green ball?

A) 13/13
B) 10/20
C) 13/20
D) 7/20

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 10+7+3. Non-green = 10+3.

\(P(\text{not green}) = \frac{10+3}{10+7+3} = 13/20\)

Q169. A bag contains 4 red, 9 green, and 9 blue balls. What is the probability of NOT drawing a green ball?

A) 4/22
B) 13/13
C) 13/22
D) 9/22

Difficulty: Easy-Medium · Topic: Complementary probability

Solution

Total = 4+9+9. Non-green = 4+9.

\(P(\text{not green}) = \frac{4+9}{4+9+9} = 13/22\)

Q170. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a club.

A) 13/13
B) 14/52
C) 13/52
D) 39/52

Difficulty: Easy-Medium · Topic: Probability with playing cards

Solution

Total cards = 52.

Number of clubs = 13

P(club) = 13/52

Q171. A bag contains 3 red, 5 white and 4 black balls. A ball is drawn at random. Find the probability that it is (i) red, (ii) not black.

Difficulty: Medium · Topic: Classical Probability

Solution

Total = 12. (i) P(red) = 3/12 = 1/4. (ii) P(not black) = 8/12 = 2/3.

Q172. A box contains 5 red, 4 green and 7 white marbles. One marble is drawn. What is the probability of it being (i) green or white, (ii) neither red nor green?

Difficulty: Medium · Topic: Classical Probability

Solution

Total = 16. (i) Green or white = 4+7 = 11. P = 11/16. (ii) Neither red nor green = white = 7. P = 7/16.

Q173. A card is drawn from a deck of 52 cards. Find the probability of getting (i) a face card, (ii) a red card, (iii) a black king.

Difficulty: Medium · Topic: Classical Probability

Solution

(i) Face cards = 12. P = 12/52 = 3/13.

(ii) Red cards = 26. P = 1/2.

(iii) Black kings = 2. P = 2/52 = 1/26.

Q174. Two dice are thrown together. Find the probability of getting a sum of 7.

Difficulty: Medium · Topic: Classical Probability

Solution

Favourable: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes. Total = 36. P = 6/36 = 1/6.

Q175. Two dice are thrown. Find the probability that the sum is at least 9.

Difficulty: Medium · Topic: Classical Probability

Solution

Sum ≥ 9: Sum 9: (3,6),(4,5),(5,4),(6,3)=4. Sum 10: (4,6),(5,5),(6,4)=3. Sum 11: (5,6),(6,5)=2. Sum 12: (6,6)=1. Total = 10. P = 10/36 = 5/18.

Q176. A number is selected at random from 1 to 20. Find P(prime number).

Difficulty: Medium · Topic: Classical Probability

Solution

Primes 1-20: {2,3,5,7,11,13,17,19} = 8. P = 8/20 = 2/5.

Q177. 12 defective pens are accidentally mixed with 132 good ones. One pen is drawn at random. Find the probability that it is not defective.

Difficulty: Medium · Topic: Classical Probability

Solution

Total = 144. Good = 132. P = 132/144 = 11/12.

Q178. Three unbiased coins are tossed. Find the probability of (i) two heads, (ii) at most two heads, (iii) at least two heads.

Difficulty: Medium · Topic: Classical Probability

Solution

S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT} = 8.

(i) Two heads: {HHT,HTH,THH} = 3. P = 3/8.

(ii) At most 2 heads (0,1,2): all except HHH = 7. P = 7/8.

(iii) At least 2 heads (2,3): {HHT,HTH,THH,HHH} = 4. P = 4/8 = 1/2.

Q179. Two dice are thrown simultaneously. What is the probability of getting a sum of 12?

A) 1/12
B) 2/36
C) 1/36
D) 12/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 12:

Number of ways = 1/36 (first part)

Probability = 1/36

Q180. Two dice are thrown simultaneously. What is the probability of getting a sum of 8?

A) 6/36
B) 5/12
C) 5/36
D) 8/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 8:

Number of ways = 5/36 (first part)

Probability = 5/36

Q181. Two dice are thrown simultaneously. What is the probability of getting a sum of 4?

A) 4/36
B) 3/36
C) 3/12
D) N/A (1)

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 4:

Number of ways = 3/36 (first part)

Probability = 3/36

Q182. Two dice are thrown simultaneously. What is the probability of getting a sum of 10?

A) 3/36
B) 3/12
C) 4/36
D) 10/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 10:

Number of ways = 3/36 (first part)

Probability = 3/36

Q183. Two dice are thrown simultaneously. What is the probability of getting a sum of 11?

A) 2/12
B) 2/36
C) 3/36
D) 11/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 11:

Number of ways = 2/36 (first part)

Probability = 2/36

Q184. Two dice are thrown simultaneously. What is the probability of getting a sum of 7?

A) 7/36
B) 6/36
C) 6/12
D) N/A (1)

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 7:

Number of ways = 6/36 (first part)

Probability = 6/36

Q185. Two dice are thrown simultaneously. What is the probability of getting a sum of 2?

A) 1/12
B) 1/36
C) N/A (1)
D) 2/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 2:

Number of ways = 1/36 (first part)

Probability = 1/36

Q186. Two dice are thrown simultaneously. What is the probability of getting a sum of 3?

A) 3/36
B) 2/12
C) N/A (1)
D) 2/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 3:

Number of ways = 2/36 (first part)

Probability = 2/36

Q187. Two dice are thrown simultaneously. What is the probability of getting a sum of 5?

A) N/A (1)
B) 4/12
C) 4/36
D) 5/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 5:

Number of ways = 4/36 (first part)

Probability = 4/36

Q188. Two dice are thrown simultaneously. What is the probability of getting a sum of 6?

A) 5/12
B) 5/36
C) N/A (1)
D) 6/36

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 6:

Number of ways = 5/36 (first part)

Probability = 5/36

Q189. Two dice are thrown simultaneously. What is the probability of getting a sum of 9?

A) 9/36
B) 4/36
C) 5/36
D) 4/12

Difficulty: Medium · Topic: Probability with two dice

Solution

Total outcomes = 36. Favourable outcomes for sum 9:

Number of ways = 4/36 (first part)

Probability = 4/36

Q190. A game of chance consists of spinning an arrow on a circular board divided into 8 equal parts numbered 1-8. What is the probability that it will point at (i) 8, (ii) an odd number, (iii) a number greater than 2?

Difficulty: Medium-Hard · Topic: Classical Probability

Solution

(i) P(8) = 1/8.

(ii) Odd: {1,3,5,7} = 4. P = 4/8 = 1/2.

(iii) Greater than 2: {3,4,5,6,7,8} = 6. P = 6/8 = 3/4.

Q191. A card is drawn from a deck. Find the probability that it is neither an ace nor a king.

Difficulty: Medium-Hard · Topic: Classical Probability

Solution

Aces + Kings = 8. P(ace or king) = 8/52 = 2/13. P(neither) = 1−2/13 = 11/13.

Q192. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn. What is the probability that it is not green?

Difficulty: Medium-Hard · Topic: Classical Probability

Solution

Total = 20. Not green = 12. P = 12/20 = 3/5.

Q193. Two dice are thrown simultaneously. Find the probability that the sum is a perfect square.

Difficulty: Medium-Hard · Topic: Classical Probability

Solution

Perfect squares possible: 4, 9. (Sum range 2-12)

Sum 4: (1,3),(2,2),(3,1) = 3. Sum 9: (3,6),(4,5),(5,4),(6,3) = 4. Total = 7.

P = 7/36.

Q194. A box contains 90 discs numbered 1-90. One disc is drawn at random. Find the probability that it bears (i) a two-digit number, (ii) a perfect square number, (iii) a number divisible by 5.

Difficulty: Hard · Topic: Classical Probability

Solution

(i) Two-digit: 10-90 = 81 numbers. P = 81/90 = 9/10.

(ii) Perfect squares: 1,4,9,16,25,36,49,64,81 = 9. P = 9/90 = 1/10.

(iii) Divisible by 5: 5,10,15,...,90 = 18 numbers. P = 18/90 = 1/5.

Chapter 14: Probability

Important Formulas

Solved Questions

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution