Page 1 PROBABILITY ASSIGNMENT 1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is : (A) 1/11 (B) 1/33 (C) 2/33 (D) None of these 2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6 respectively, then probabilities that none of them is selected is : (A) 1/24 (B) 5/12 (C) 5/8 (D) 19/12 3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same colour is : (A) 5/108 (B) 1/6 (C) 5/18 (D) 4/9 4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn ticket has a number 5 or a multiple of 5 is : (A) 1/10 (B) 1/5 (C) 1/25 (D) 1/2 5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be woman is : (A) 25/39 (B) 14/39 (C) 5/13 (D) 10/13 6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that both are aces is : (A) 2/13 (B) 1/51 (C) 1/221 (D) None of these 7. Three coins are tossed together. The probability of atleast two heads is : (A) 1/8 (B) 3/8 (C) 1/2 (D) 1/4 8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is (A) 1/18 (B) 1/12 (C) 1/9 (D) none of these 9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is (A) 1/4 (B) 1/2 (C) 3/4 (D) 1/3 10. The probability that a leap year selected at random contains 53 Sundays is (A) 7/366 (B) 26/183 (C) 1/7 (D) 2/7 GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1 Page 2 PROBABILITY ASSIGNMENT 1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is : (A) 1/11 (B) 1/33 (C) 2/33 (D) None of these 2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6 respectively, then probabilities that none of them is selected is : (A) 1/24 (B) 5/12 (C) 5/8 (D) 19/12 3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same colour is : (A) 5/108 (B) 1/6 (C) 5/18 (D) 4/9 4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn ticket has a number 5 or a multiple of 5 is : (A) 1/10 (B) 1/5 (C) 1/25 (D) 1/2 5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be woman is : (A) 25/39 (B) 14/39 (C) 5/13 (D) 10/13 6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that both are aces is : (A) 2/13 (B) 1/51 (C) 1/221 (D) None of these 7. Three coins are tossed together. The probability of atleast two heads is : (A) 1/8 (B) 3/8 (C) 1/2 (D) 1/4 8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is (A) 1/18 (B) 1/12 (C) 1/9 (D) none of these 9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is (A) 1/4 (B) 1/2 (C) 3/4 (D) 1/3 10. The probability that a leap year selected at random contains 53 Sundays is (A) 7/366 (B) 26/183 (C) 1/7 (D) 2/7 GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1 11. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is (A) 47/66 (B) 10/33 (C) 5/22 (D) none of these 12. Three identical dice are rolled. The probability that the same number will appear on each of them is (A) 1/6 (B) 1/18 (C) 1/36 (D) none of these 13. The probability that a man aged 50 years will die in a year is p. The probability that out of n men A 1 , A 2 , …., A n each aged 50 years, A 1 will die and be first to die is (A) 1 – (1 – p) n (B) [1 – (1 – p) n ] / n 2 (C) [1 – (1 – p) n ] / n (D) none of these 14. A bag contains 3 white and 4 red balls. Another bag contains 5 white and 7 red balls. A ball is taken out of the first bag and put in to the second. A ball is then taken out of the second bag. The probability that it is a red ball is (A) 1/3 (B) 53/91 (C) 32/91 (D) none of these 15. A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is (A) 1/3 (B) 8/15 (C) 5/13 (D) 2/3 16. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is (A) 1/5 (B) 2/5 (C) 1/10 (D) none of these 17. The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India's second win occurs at the third test is (A) 1/8 (B) 1/4 (C) 1/2 (D) 2/3 18. The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then P( A ) + P( B ) = (A) 1.8 (B) 0.6 (C) 1.1 (D) 1.4 19. Both A and B throw a dice. The chance that B throws a number higher than that thrown by A is (A) 1/2 (B) 21/36 (C) 15/36 (D) none of these 20. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is (A) 291/364 (B) 371/464 (C) 471/502 (D) 459/512 GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 2 Page 3 PROBABILITY ASSIGNMENT 1. A positive integer is chosen at random. The probability that sum of the digits of its square is 33 is : (A) 1/11 (B) 1/33 (C) 2/33 (D) None of these 2. Two persons A and B appear in an interview for two vacancies. If the probability of their selection are 1/4 and 1/6 respectively, then probabilities that none of them is selected is : (A) 1/24 (B) 5/12 (C) 5/8 (D) 19/12 3. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are in the same colour is : (A) 5/108 (B) 1/6 (C) 5/18 (D) 4/9 4. Tickets are numbered 1 to 100. They are well–shuffled and a ticket is drawn at random. Probability that the drawn ticket has a number 5 or a multiple of 5 is : (A) 1/10 (B) 1/5 (C) 1/25 (D) 1/2 5. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be woman is : (A) 25/39 (B) 14/39 (C) 5/13 (D) 10/13 6. From a well shuffled pack of playing cards, two cards are drawn one by one with replacement. The probability that both are aces is : (A) 2/13 (B) 1/51 (C) 1/221 (D) None of these 7. Three coins are tossed together. The probability of atleast two heads is : (A) 1/8 (B) 3/8 (C) 1/2 (D) 1/4 8. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is (A) 1/18 (B) 1/12 (C) 1/9 (D) none of these 9. The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is (A) 1/4 (B) 1/2 (C) 3/4 (D) 1/3 10. The probability that a leap year selected at random contains 53 Sundays is (A) 7/366 (B) 26/183 (C) 1/7 (D) 2/7 GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 1 11. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is (A) 47/66 (B) 10/33 (C) 5/22 (D) none of these 12. Three identical dice are rolled. The probability that the same number will appear on each of them is (A) 1/6 (B) 1/18 (C) 1/36 (D) none of these 13. The probability that a man aged 50 years will die in a year is p. The probability that out of n men A 1 , A 2 , …., A n each aged 50 years, A 1 will die and be first to die is (A) 1 – (1 – p) n (B) [1 – (1 – p) n ] / n 2 (C) [1 – (1 – p) n ] / n (D) none of these 14. A bag contains 3 white and 4 red balls. Another bag contains 5 white and 7 red balls. A ball is taken out of the first bag and put in to the second. A ball is then taken out of the second bag. The probability that it is a red ball is (A) 1/3 (B) 53/91 (C) 32/91 (D) none of these 15. A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is (A) 1/3 (B) 8/15 (C) 5/13 (D) 2/3 16. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is (A) 1/5 (B) 2/5 (C) 1/10 (D) none of these 17. The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India's second win occurs at the third test is (A) 1/8 (B) 1/4 (C) 1/2 (D) 2/3 18. The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then P( A ) + P( B ) = (A) 1.8 (B) 0.6 (C) 1.1 (D) 1.4 19. Both A and B throw a dice. The chance that B throws a number higher than that thrown by A is (A) 1/2 (B) 21/36 (C) 15/36 (D) none of these 20. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is (A) 291/364 (B) 371/464 (C) 471/502 (D) 459/512 GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 2 21. The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is (A) 1 (B) 1 – (0.7) 10 (C) (0.7) 10 (D) (0.3) 10 22. A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Then (A) P (A) = 1/2, P (B) = 1/3 (B) P (A) = 1/2, P (B) = 1/6 (C) P (A) = 1/3, P (B) = 1/2 (D) none of these 23. In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class, has passed in only one subject is (A) 13/25 (B) 3/25 (C) 17/25 (D) 8/25 24. A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is (A) 3/5 (B) 3/10 (C) 4/5 (D) 1/2 25. 3 mangoes and 3 apples are in a box. If 2 fruits are chosen at random, the probability that one is a mango and the other is an apple is (A) 3/5 (B) 5/6 (C) 1/36 (D) none of these 26. A father has 3 children with at least one boy. The probability that he has 2 boys and one girl is (A) 1/4 (B) 1/3 (C) 2/3 (D) none of these 27. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is (A) 25/39 (B) 14/39 (C) 5/13 (D) 10/13 28. Two events A and B have probability 0.25 and 0.50. The probability that both occur simultaneously is 0.14. The probability that neither A nor B occurs is (A) 0.75 (B) 0.61 (C) 0.39 (D) none of these 29. If A and B are independent events and P (A ? B) = 9/10, P (B) = 4/10, then P (A) = (A) 1/6 (B) 5/6 (C) 1/9 (D) none of these 30. A, B, C in order toss a coin. The first one to throw a head wins. Assuming the game continues indefinite their respective chances of winning the game are (A) 4/7, 2/7, 1/7 (B) 1/7, 4/7, 2/7 (C) 2/7, 4/7, 1/7 (D) none of these GIITJEE CHANDIGARH LIMITED SCO 382, Sector 37–D, Chandigarh – 160 036 Ph: 3290959 P – 3Read More

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