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Math Topic - Probability

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Published in: Statistics
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PBI I / Jalandhar

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  1. PBI PBI INSTITUTE 1. Probability In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? A. c. Solution 1/10 2/7 B. D. = 10/ (10+25) 10/ 35 2/7. 2/5 5/7 P(getting a prize) 2. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? A. c. Solution 3/4 1/8 B. D. 4/7 3/7 Total number of balls = 14. Number of white balls P(drawing a white ball) — - 8/14 3. From a pack of 52 cards, two cards are drawn together at random.What is the probability of both the cards being kings? A. c. Solution 1/15 35/256 B. D. 25/57 1/221 Let S be the sample space. Then, — 52C2
  2. PBI event of getting 2 kings out of 4. _ 4C2 PBI INSTITUTE Let E = 4. = 1326. = 6/ 1326 = 1/221. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5? A. c. Solution 1/2 8/15 B. D. 2/5 9/20 Here 19,20). Let E=event of getting a multiple of 5. = 9/20. What is the probability of getting a sum 9 from two throws of a dice? A. c. Solution 1/6 1/9 B. D. = 36. 1/8 1/12 In two throws of a die, n(S) Let E = event of getting a sum 9= = 4/36
  3. PBI PBI INSTITUTE 6. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? A. 2/3 c. 7/19 Solution Total number of balls D. 8/21 = 21. Let E = event that the ball drawn is neither red nor green =event that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/21. 7. In a single throw of a dice, what is the probability of getting a number greater than 4? A. 1/2 c. 2/3 Solution B. 1/3 D. 1/4 When a dice is thrown, we have S= {1,2,3,4,5,6}. Let E = event of getting a number greater than 4= {5, 6}. = 2/6 = 1/3. 9. Three unbiased coins are tossed. What is the probability of getting at most two heads? A. 3/4 c. 3/8 Solution Here S = {TTT, TTH, THT, HIT, THI-I, I-ITH HHT, HHH} Let E = event of getting at most two heads. Then E = {ITT, 7TH, THT, HIT, THH, I-ITH HHT}. B. 1/4 D. 7/8 10. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is A. 1/13 c. 1/26 Solution Here, n(S) = 52 Let E = event of getting a queen of club or a king of heart. B. 2/13 D. 1/52
  4. PBI Then, n(E) = 2. PBI INSTITUTE 11. = 2/52 1/26. In a simultaneous of two dice, what is the probability of getting a toatl of 10 or 11? c. 7/12 Solution B. 1/6 D. 5/36 In a simultaneous throw of two dice,we have n(S)= (6>
  5. PBI Then, n(E) Therefore, 15. Solution Here = 14. An unbiased die is tossed. 1/2 A. c. 1/3 PBI INSTITUTE = 16. = 14/ 36 = 7/18. Find the probability of getting a multiple of 3. B. 1/4 D. 2/4 Let E be the event of getting a multiple of 3. Then, E = {3,6}. = 2/6 16. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is A. 4/19 c. 12/19 Solution P( None is defective) P( at least one is defective) B. 7/19 D. 21/95 = 16C2 / 20C2 = 12/19. = (1- 12/19) = 7/19.

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