Probability Exercises

Question Bank

Abhishek Jain

1. From a pack of 52 cards, two cards are drawn at random. What is the probability that either both are red or both are queens is Ans: 2. A box contains 20 balls bearing numbers 1, 2, 3 .. 20. A ball is drawn at random from the box. What is the probability that the number on the ball is divisible by 2 or 3? Ans: 3. A bag contains 2 red, 5 blue and 7 green balls. A ball is drawn at random. What is the probability that it is either a blue or a green ball? Ans: 4. From a pack of cards two cards are drawn at random. What is the probability that either both are kings or both are queens? Ans: 5. There are 8 blue and 4 white balls in a bag. A ball is drawn at random. Without replacing it another ball is drawn. Find the probability that both the balls drawn are blue Ans:

6. There are 5 green and 6 black balls in a bag. A ball is drawn at random with replacement. Find the probability that both the balls drawn are black Ans: 7. A speaks truth in 60% of the cases and B in 80% if the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident? Ans: 44% 8. A lot of 12 bulbs contains 4 defective bulbs. Three bulbs are drawn at random from the lot, one after the other. The probability that all three are non-defective is Ans: 14/55 9. 100 students appeared for two examinations, 60 passed the first, 50 passed the second and 30 passed both. The probability that a student selected at random has failed in both examinations is Ans: 0.2 10. A and B stand in a ring with 11 other persons. If the arrangement of the 13 persons is at random, then the probability that there are exactly 3 persons between A and B is Ans: 1/6 11. A candidate is selected for interview for three posts. For the first post there are 5 candidates for the second there are

8 and for the third there are 7. What are the chance for his setting at least one post? Ans: 2/5 12. In a 6 faced die with numbers 1 to 6 inscribed. Find the probability of getting a 2 digit number which is prime on adding 2 successive throws of the die Ans: 1/3 13. Out of 20 consecutive positive integers, two are chosen at random. The probability that their sum is odd is Ans: 10/19 14. When two dice are rolled, what is the probability that the sum of the numbers appeared on them is 11? Ans: 1/18 15. The probability of drawing a red card from a deck of playing cards, is Ans: 1/2 16. Five coins are tossed at a time. Then the probability of obtaining at least one tail is Ans: 31/32 17. If a 4 digit number is formed at random using the digits 1, 3, 5, 7, 9 without repetition, then the probability that it is

divisible by 5 is Ans: 1/5 18. The probability of getting a composite number when a six-faced unbiased die is tossed, is Ans: 1/3 19. Two unbiased dice are thrown simultaneously. The probability of getting the sum divisible by 3 is Ans: 12/26 20. A number is selected at random from the set {1, 2, 3 .. 50}. The probability that n is a prime is Ans: 0.3 21. If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is Ans: 3/8 22. Let E be the set of all integers with 1 in their unit place. The probability that a number chosen {2, 3, 4 . 50} is an element of E is Ans: 4/49 23. A number x is chosen at random from {1, 2, . 10}.The probability that x satisfies the equation (x-3) (x-6) (x-10)=0 is Ans: 3/10

24. A person gets as many rupees as the number he gets when an unbiased six-faced die is thrown. If two such dice are thrown the probability of getting Rs. 10 is Ans: 1/12 25. A bag contains 3 red balls, 4 white balls and 7 black balls. The probability of drawing a red or a black ball is Ans: 5/7 26. If a die is thrown, then the probability of getting an even number or a number greater than 3, is Ans: 2/3 27. If two dice are thrown simultaneously, then the probability of having 6 on first die and any number other than 6 on other die is Ans: 5/36 28. In a single throw of two dice, find the probability of getting a total of 3 or 5 Ans: 1/6 29. A box contains 36 tickets numbered 1 to 36, one ticket drawn at random. Find the probability that the number on the ticket is either divisible by 3 or is a perfect square Ans: 4/9

30. The letters B, G, I, N, R are rearranged to form the word BRING. Find its probability Ans: 1/120 31. A box of electronic diode contains 120 standard and 80 sub-standard ones. Two diodes are taken at random. What is the probability that one is standard and the other is sub-standard? Ans: 96/199 32. A box contains 20 white, 30 black, 40 blue and 30 red balls. Compute the probability that one of the balls extracted at random from the box turns out to be white, black or red Ans: 2/3 33. If one rolls a fair-sided die twice, what is the probability that the die will land on the same number on both the occasions? Ans: 1/6 34. If seven coins are tossed, what is the probability of obtaining at least 2 heads? Ans: 15/16 35. A bag contains 4 red, 5 blue and 6 black balls. If one ball is drawn at random, find the probability that it is not a black ball Ans: 3/5

36. A coin is tossed twice. Find the probability of getting no head Ans: 1/4 37. Three unbiased coins are tossed. Find the probability of getting at least two heads Ans: 1/2 38. If two dice are thrown together, what is the probability of the sum being less than 6, on the side facing up? Ans: 5/8 39. From a pack of 52 cards, what is the probability of picking a spade card if only one card is drawn? Ans: 0.25 40. If a bag contains 5 yellow and 6 red balls and 2 balls are drawn out together, what are the odds against all balls being red? Ans: 8/11 41. What is the probability that a randomly chosen 2 digit number is divisible by 5? Ans: 1/5 42. There are 16 candidates for three openings in a company. If five of them are women, what is the probability

that exactly one woman would be chosen for the job? Ans: 55/224 43. A school has 4 labs and 10 classrooms. If a student can go to any of these rooms, what is the probability that the students entered a particular room? Ans: 1/14 44. If the letters of the word English are rearranged, what is the probability that a word will start with a vowel? Ans: 2/7 45. Reshma decided to get married and wanted to inform 3 out of her 5 friends first, before conveying to everyone else. If Sushma is one among her 5 friends, what is the probability that Sushma will be among the first 3 to hear about Reshmas wedding? Ans: 3/5 46. When four coins are tossed simultaneously, what is the probability of getting exactly two heads? Ans: 3/8 47. From a pack of cards, if 4 random cards are drawn, what is the probability that each card is from a different suit? Ans: 134/52C4

48. Find the probability of getting a number less than five when a die is rolled? Ans: 2/3 49. Two dice are thrown, find the probability of getting an even total on them Ans: 1/2 50. Three dice are thrown, find the probability of getting a sum greater than 17 on their faces Ans: 1/216 51. If three coins are tossed, find the probability of the event showing exactly one Tail on them Ans: 3/8 52. Two coins are tossed. Find the probability that two tails result, given that there is atleast one tail Ans: 1/3 53. Two men A and B run a race. If the probability of As wins is twice that of B. Find the probability of Bs win Ans: 1/3 54. Find the probability that vowel selected at random from an English book is a 0 Ans: 1/5

55. In a single throw with two dice, find the probability of throwing a 10 Ans: 1/12 56. When three coins are tossed simultaneously find the probability of getting one tail Ans: 3/8 57. Two dice are thrown simultaneously. Find the probability that the sum of the numbers is at most 4 Ans: 1/6 58. Find the probability that a non-leap year should have 52 Tuesdays Ans: 6/7 59. A single letter is selected at random from the word CONICS. Find the probability that it is a vowel Ans: 1/3 60. If 3 dice are rolled, find the total number of exhaustive out comes Ans: 63 61. If four students are chosen at random, find the probability that no two of them were born on the same day

of the week Ans: 120/343 62. An integer is chosen from 3 to 17 what is the probability that it is prime? Ans: 2/5 63. Two dice are thrown together. Find the probability that we get a total of 10 Ans: 1/12 64. Find the probability of getting an odd number in throw of an unbiased die? Ans: 1/2 65. Three coins are tossed. Find the probability of getting atleast two tail Ans: 1/2 66. Find the probability of getting a king or a Queen in a single draw from a well shuffled pack of playing cards Ans: 2/13 Directions (67 - 69): One card is drawn from a pack of 52 cards, each card being equally likely to be drawn

67. Find the probability that the card drawn is red Ans: 1/2 68. Find the probability that the card drawn is a king Ans: 1/13 69. Find the probability that the card drawn is red and a king Ans: 1/26 70. One card is drawn at random from a pack of cards. Find the probability that the card drawn is either a king or a queen? Ans: 2/13