OU All In One

Probability questions

Dice, coins, cards and balls.

1. A card is drawn from a well-shuffled pack of 52. What is the probability that it is a heart?

  1. 7/26
  2. 1/2
  3. 1/13
  4. 1/4
Answer

D. 1/4 13 favourable cards out of 52 = 1/4.

2. A bag has 8 red, 3 blue and 2 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 8/13
  2. 2/13
  3. 3/10
  4. 3/13
Answer

D. 3/13 3 blue out of 13 balls = 3/13.

3. A card is drawn from a well-shuffled pack of 52. What is the probability that it is a face card?

  1. 3/13
  2. 1/13
  3. 1/4
  4. 1/2
Answer

A. 3/13 12 favourable cards out of 52 = 3/13.

4. Two dice are thrown. What is the probability that the sum is 7?

  1. 7/36
  2. 1/12
  3. 1/2
  4. 1/6
Answer

D. 1/6 6 of the 36 outcomes give 7, so 1/6.

5. 3 coins are tossed. What is the probability of getting at least one head?

  1. 1/8
  2. 7/8
  3. 1/2
  4. 3/8
Answer

B. 7/8 P(no heads) = 1/8, so P(at least one) = 1 − 1/8 = 7/8.

6. A card is drawn from a well-shuffled pack of 52. What is the probability that it is an ace or a king?

  1. 1/4
  2. 1/13
  3. 2/13
  4. 9/52
Answer

C. 2/13 8 favourable cards out of 52 = 2/13.

7. A card is drawn from a well-shuffled pack of 52. What is the probability that it is a king?

  1. 1/13
  2. 1/4
  3. 1/2
  4. 5/52
Answer

A. 1/13 4 favourable cards out of 52 = 1/13.

8. A card is drawn from a well-shuffled pack of 52. What is the probability that it is a red card?

  1. 1/2
  2. 1/4
  3. 1/13
  4. 27/52
Answer

A. 1/2 26 favourable cards out of 52 = 1/2.

9. A bag has 3 red, 7 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/11
  2. 1/11
  3. 7/4
  4. 7/11
Answer

D. 7/11 7 blue out of 11 balls = 7/11.

10. Two dice are thrown. What is the probability that the sum is 8?

  1. 1/6
  2. 5/36
  3. 1/12
  4. 5/12
Answer

B. 5/36 5 of the 36 outcomes give 8, so 5/36.

11. 2 coins are tossed. What is the probability of getting at least one head?

  1. 3/4
  2. 1/4
  3. 1/18
  4. 1/2
Answer

A. 3/4 P(no heads) = 1/4, so P(at least one) = 1 − 1/4 = 3/4.

12. A bag has 3 red, 8 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/1
  2. 5/16
  3. 3/16
  4. 1/2
Answer

D. 1/2 8 blue out of 16 balls = 1/2.

13. Two dice are thrown. What is the probability that the sum is 5?

  1. 1/12
  2. 1/6
  3. 5/36
  4. 1/9
Answer

D. 1/9 4 of the 36 outcomes give 5, so 1/9.

14. A bag has 8 red, 8 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 4/7
  2. 4/11
  3. 9/22
  4. 3/11
Answer

B. 4/11 8 blue out of 22 balls = 4/11.

15. Two dice are thrown. What is the probability that the sum is 10?

  1. 1/4
  2. 1/6
  3. 1/12
  4. 1/9
Answer

C. 1/12 3 of the 36 outcomes give 10, so 1/12.

16. A bag has 4 red, 5 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/1
  2. 1/2
  3. 2/5
  4. 1/10
Answer

B. 1/2 5 blue out of 10 balls = 1/2.

17. Two dice are thrown. What is the probability that the sum is 6?

  1. 5/12
  2. 5/36
  3. 1/6
  4. 1/12
Answer

B. 5/36 5 of the 36 outcomes give 6, so 5/36.

18. A bag has 5 red, 2 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 2/13
  2. 6/13
  3. 2/11
  4. 5/13
Answer

A. 2/13 2 blue out of 13 balls = 2/13.

19. Two dice are thrown. What is the probability that the sum is 9?

  1. 5/36
  2. 1/12
  3. 1/6
  4. 1/9
Answer

D. 1/9 4 of the 36 outcomes give 9, so 1/9.

20. A bag has 6 red, 5 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 5/12
  2. 5/17
  3. 7/36
  4. 6/17
Answer

B. 5/17 5 blue out of 17 balls = 5/17.

21. Two dice are thrown. What is the probability that the sum is 4?

  1. 1/12
  2. 1/6
  3. 1/4
  4. 1/9
Answer

A. 1/12 3 of the 36 outcomes give 4, so 1/12.

22. A bag has 4 red, 7 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 5/16
  2. 1/4
  3. 7/16
  4. 7/9
Answer

C. 7/16 7 blue out of 16 balls = 7/16.

23. Two dice are thrown. What is the probability that the sum is 3?

  1. 1/6
  2. 7/36
  3. 1/18
  4. 1/12
Answer

C. 1/18 2 of the 36 outcomes give 3, so 1/18.

24. A bag has 4 red, 6 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/4
  2. 3/8
  3. 7/16
  4. 3/5
Answer

B. 3/8 6 blue out of 16 balls = 3/8.

25. Two dice are thrown. What is the probability that the sum is 11?

  1. 1/18
  2. 1/12
  3. 1/4
  4. 1/6
Answer

A. 1/18 2 of the 36 outcomes give 11, so 1/18.

26. A bag has 3 red, 2 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/10
  2. 1/5
  3. 1/4
  4. 1/2
Answer

B. 1/5 2 blue out of 10 balls = 1/5.

27. A bag has 3 red, 7 blue and 4 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/14
  2. 1/2
  3. 2/7
  4. 1/1
Answer

B. 1/2 7 blue out of 14 balls = 1/2.

28. A bag has 7 red, 6 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/4
  2. 3/7
  3. 1/14
  4. 1/2
Answer

B. 3/7 6 blue out of 14 balls = 3/7.

29. A bag has 4 red, 8 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 4/9
  2. 4/5
  3. 1/3
  4. 2/9
Answer

A. 4/9 8 blue out of 18 balls = 4/9.

30. A bag has 8 red, 2 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/11
  2. 2/11
  3. 8/11
  4. 2/9
Answer

B. 2/11 2 blue out of 11 balls = 2/11.

31. A bag has 6 red, 4 blue and 2 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/6
  2. 1/2
  3. 5/12
  4. 1/3
Answer

D. 1/3 4 blue out of 12 balls = 1/3.

32. A bag has 2 red, 2 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/3
  2. 2/9
  3. 5/9
  4. 2/7
Answer

B. 2/9 2 blue out of 9 balls = 2/9.

33. A bag has 5 red, 8 blue and 3 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/16
  2. 1/1
  3. 1/2
  4. 5/16
Answer

C. 1/2 8 blue out of 16 balls = 1/2.

34. A bag has 5 red, 8 blue and 2 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 2/15
  2. 1/3
  3. 8/7
  4. 8/15
Answer

D. 8/15 8 blue out of 15 balls = 8/15.

35. A bag has 8 red, 3 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 5/16
  2. 3/16
  3. 3/13
  4. 1/2
Answer

B. 3/16 3 blue out of 16 balls = 3/16.

36. A bag has 2 red, 5 blue and 3 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/5
  2. 1/2
  3. 3/10
  4. 1/1
Answer

B. 1/2 5 blue out of 10 balls = 1/2.

37. A bag has 2 red, 5 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/2
  2. 5/7
  3. 1/6
  4. 5/12
Answer

D. 5/12 5 blue out of 12 balls = 5/12.

38. A bag has 3 red, 3 blue and 3 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 4/9
  2. 1/2
  3. 1/3
  4. 1/12
Answer

C. 1/3 3 blue out of 9 balls = 1/3.

39. A bag has 6 red, 5 blue and 4 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/3
  2. 2/5
  3. 1/2
  4. 4/15
Answer

A. 1/3 5 blue out of 15 balls = 1/3.

40. A bag has 5 red, 4 blue and 4 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 4/9
  2. 5/13
  3. 4/13
  4. 2/3
Answer

C. 4/13 4 blue out of 13 balls = 4/13.

41. A bag has 5 red, 7 blue and 4 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 5/16
  2. 7/9
  3. 7/16
  4. 1/4
Answer

C. 7/16 7 blue out of 16 balls = 7/16.

42. A bag has 2 red, 2 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/4
  2. 1/5
  3. 3/10
  4. 3/5
Answer

B. 1/5 2 blue out of 10 balls = 1/5.

43. A bag has 4 red, 6 blue and 5 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/3
  2. 4/15
  3. 2/5
  4. 2/3
Answer

C. 2/5 6 blue out of 15 balls = 2/5.

44. A bag has 5 red, 5 blue and 4 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/7
  2. 2/7
  3. 5/9
  4. 5/14
Answer

D. 5/14 5 blue out of 14 balls = 5/14.

45. A bag has 7 red, 5 blue and 2 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/2
  2. 5/9
  3. 5/14
  4. 1/7
Answer

C. 5/14 5 blue out of 14 balls = 5/14.

46. A bag has 8 red, 8 blue and 3 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 9/19
  2. 8/11
  3. 8/19
  4. 3/19
Answer

C. 8/19 8 blue out of 19 balls = 8/19.

47. A bag has 5 red, 8 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 1/14
  2. 4/3
  3. 4/7
  4. 5/14
Answer

C. 4/7 8 blue out of 14 balls = 4/7.

48. A bag has 3 red, 8 blue and 2 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 8/13
  2. 2/13
  3. 3/13
  4. 8/5
Answer

A. 8/13 8 blue out of 13 balls = 8/13.

49. A bag has 5 red, 5 blue and 6 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 5/16
  2. 3/8
  3. 2/9
  4. 5/11
Answer

A. 5/16 5 blue out of 16 balls = 5/16.

50. A bag has 3 red, 3 blue and 1 green balls. One ball is drawn at random. What is the probability that it is blue?

  1. 3/4
  2. 4/7
  3. 3/7
  4. 1/7
Answer

C. 3/7 3 blue out of 7 balls = 3/7.

51. A bag contains 4 red and 12 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 1/4
  2. 3/4
  3. 1/3
  4. 1/16
Answer

A. 1/4 Favourable outcomes = 4 red balls; total = 4 + 12 = 16. Probability = 4/16 = 1/4.

52. A bag contains 10 red and 13 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 10/23
  2. 13/23
  3. 10/13
  4. 1/23
Answer

A. 10/23 Favourable outcomes = 10 red balls; total = 10 + 13 = 23. Probability = 10/23 = 10/23.

53. A bag contains 14 red and 5 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 14/19
  2. 5/19
  3. 14/5
  4. 1/19
Answer

A. 14/19 Favourable outcomes = 14 red balls; total = 14 + 5 = 19. Probability = 14/19 = 14/19.

54. A bag contains 14 red and 8 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 7/11
  2. 4/11
  3. 7/4
  4. 1/22
Answer

A. 7/11 Favourable outcomes = 14 red balls; total = 14 + 8 = 22. Probability = 14/22 = 7/11.

55. A bag contains 14 red and 10 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 7/12
  2. 5/12
  3. 7/5
  4. 1/24
Answer

A. 7/12 Favourable outcomes = 14 red balls; total = 14 + 10 = 24. Probability = 14/24 = 7/12.

56. A bag contains 20 red and 8 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 5/7
  2. 2/7
  3. 5/2
  4. 1/28
Answer

A. 5/7 Favourable outcomes = 20 red balls; total = 20 + 8 = 28. Probability = 20/28 = 5/7.

57. A bag contains 9 red and 14 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 9/23
  2. 14/23
  3. 9/14
  4. 1/23
Answer

A. 9/23 Favourable outcomes = 9 red balls; total = 9 + 14 = 23. Probability = 9/23 = 9/23.

58. A bag contains 5 red and 3 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 5/8
  2. 3/8
  3. 5/3
  4. 1/8
Answer

A. 5/8 Favourable outcomes = 5 red balls; total = 5 + 3 = 8. Probability = 5/8 = 5/8.

59. A bag contains 5 red and 14 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 5/19
  2. 14/19
  3. 5/14
  4. 1/19
Answer

A. 5/19 Favourable outcomes = 5 red balls; total = 5 + 14 = 19. Probability = 5/19 = 5/19.

60. A bag contains 4 red and 6 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 2/5
  2. 3/5
  3. 2/3
  4. 1/10
Answer

A. 2/5 Favourable outcomes = 4 red balls; total = 4 + 6 = 10. Probability = 4/10 = 2/5.

61. A bag contains 17 red and 13 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 17/30
  2. 13/30
  3. 17/13
  4. 1/30
Answer

A. 17/30 Favourable outcomes = 17 red balls; total = 17 + 13 = 30. Probability = 17/30 = 17/30.

62. A bag contains 5 red and 8 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 5/13
  2. 8/13
  3. 5/8
  4. 1/13
Answer

A. 5/13 Favourable outcomes = 5 red balls; total = 5 + 8 = 13. Probability = 5/13 = 5/13.

Mock test

More Quantitative Aptitude topics