TEST A CHAPTER 11, PROBABILITY
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1 TEST A CHAPTER 11, PROBABILITY 1. Two fair dice are rolled. Find the probability that the sum turning up is 9, given that the first die turns up an even number. 2. Two fair dice are rolled. Find the probability that: a. They show a sum of 10. b. The first die turns up an odd number. c. Are these two events independent? Explain? 3. A certain prescription drug produces side effects in 3% of the patients. Three patients that have taken this drug are selected at random. Find the probability that: a. All three had side effects. b. None of the three had side effects. 4. Rosie has to take a Math course and an English course, both of which are available at 9 a.m., 10 a.m.,and 11 a.m. If Rosie picks a schedule at random, what is the probability that she will have Math at 9 a.m. and English at 11 a.m.? 5. The probability that a cassette tape is defective is If two tapes are selected at random, what is the probability that both are good? 6. A card is selected at random from a standard deck of 52 cards. Find the odds in favor of the card being: a. A red face card (Jack, Queen, King). b. Not a red face card. 7. The probability of an event occurring is 3/5. Find the odds: a. In favor of the event occurring. b. Against the event occurring.
2 8. The odds in favor of an event occurring are 3 to 5. Find: a. The odds against the event occurring? b. The probability that the event will not occur? 9. A single fair die is rolled twice. If exactly one six turns up, you receive $5 and, if two sixes turn up, you receive $10; otherwise, you get nothing. What is a fair price to pay for playing this game? 10. The probabilities of being an "instant winner" of $25 or $50 in a certain lottery are and 1, respectively. What is the mathematical 1000 expectation of being an "instant winner" of $25 or $50? 11. A single fair die is rolled. Find the probability of obtaining: a. A number different from both 1 and 2. b. A number greater than or equal to A box contains 2 red balls, marked R 1, and R 2, and 3 white balls, marked W 1, W 2, and W 3. a. Two balls are drawn in succession without replacement. Find the number of elements in the sample space for this experiment. (We are interested in which balls are drawn and the order in which they are drawn.) b. Do Part (a) if the balls are drawn in succession with replacement. 13. A box contains 7 balls numbered from 1 to 7. If a ball is taken at random from the box, find the probability that it is: a. An even-numbered ball. b. Ball number 3. c. Not ball number 3.
3 14. Two cards are drawn at random and without replacement from a standard deck of 52 cards. Find the probability that: a. Both cards are red. b. Neither card is a Jack, Queen, or King. 15. A card is drawn at random from a standard deck of 52 cards and is then replaced. A second card is then drawn. Find the probability that: a. Both cards are red. b. Neither card is a King or a Queen 16. A fair coin is tossed 3 times. What is the probability of obtaining at least one head? 17. An urn contains 3 white, 3 black, and 2 red balls. Find the probability of obtaining in a single random draw: a. A white ball or a red ball. b. A ball that is not white. 18. A student estimates that the probability of his passing Chemistry or English is 0.8, the probability of his passing Chemistry is 0.7, but his probability of passing both is 0.5. What should be his estimate of the probability of his passing English? 19. Two cards are drawn in succession and without replacement from a standard deck of 52 cards. What is the probability that they are both red face cards (Jack, Queen, King)? 20. Two fair dice are rolled. Find the probability that the sum turning up is 10, given that the first die turns up 6.
4 TEST B CHAPTER 11, PROBABILITY 1. A fair die was rolled twice and an even number turned up the first time. What is the probability that the sum of the numbers turning up was 9? a. 0 b. 1/9 c. 1/6 d. 1/18 e. 1/10 2. A certain prescription drug produces side effects in 3% of the patients. Three patients who have taken this drug are selected at random. The probability that all three of these patients had side effects is a b c d e In Problem 2, the probability that none of the three patients had side effects is a b. (0.97) 2 c. (0.97) 3 d. (0.97) 4 4. Susie has to take a Math course and an English course, both of which are available at 9 a.m., 10 a.m., and 11 a.m. If Susie picks a schedule at random, the probability that she will have Math at 9 a.m. and English at 11 a.m. is a. 1/6 b. 1/3 c. 1/4 d. 3/4 e. 2/3 5. The probability that a cassette tape is defective is If two tapes are selected at random, what is the probability that both are good? a b c d. (0.03) 2 6. A card is selected at random from a standard deck of 52 cards. The odds in favor of the card being a red face card (Jack, Queen, King) are a. 23 to 3 b. 3 to 23 c. 3 to 26 d. 6 to The probability that a certain event will occur is 3/5. The odds that the event will not occur are a. 3 to 5 b. 5 to 3 c. 2 to 5 d. 2 to 3
5 8. The odds in favor of an event occurring are 3 to 5. The probability that the event will not occur is a. 3/5 b. 3/8 c. 5/3 d. 2/5 e. 5/8 9. A single fair die is rolled twice. If exactly one 6 comes up, you receive $5, and if two 6's come up, you receive $10; otherwise, you get nothing. A fair price to pay for playing this game is a. $1.67 b. $4 c. $5 d. $6 e. $ The probabilities of being an "instant winner" of $25 or $50 in a certain lottery are and , respectively. The mathematical expectation of being an "instant winner" of $25 or $50 is a. $1 b. $3.50 c. 20 cents d. 10 cents 11. A single fair die is rolled. The probability of obtaining a number different from both 1 and 2 is a. 1/6 b. 1/3 c. 2/3 d. 5/6 12. A single fair die is rolled. The probability of obtaining a number greater than or equal to 4 is a. 1/3 b. 1/2 c. 2/3 d. 5/6 13. A box contains two red balls marked R 1, and R 2, and three white balls marked W 1, W 2 and W 3. Two balls are drawn in succession and without replacement.. Suppose that we are interested in which balls and in what order they are drawn. The number of elements in the sample space for this experiment is a. 5 b. 10 c. 15 d Two cards are drawn at random and without replacement from a standard deck of 52 cards. The probability that both cards are red is a. 13/51 b. 26/51 c. 25/102 d. 1/4
6 15. If two cards are drawn at random and without replacement from a standard deck of 52 cards, the probability that neither card is a King, Queen or Jack is C(12,2) a. 10/17 b. 10/13 c. 1/40 d. C(52,2) 16. A fair coin is tossed 3 times. The probability of getting at least one head is a. 1/2 b. 3/4 c. 7/8 d. 15/ An urn contains three white balls, three black balls, and two red balls. The probability of obtaining a white or a red ball in a single draw is a. 5/8 b. 3/8 c. 1/2 d For the urn of Problem 17, the probability of obtaining a ball that is not white is a. 5/8 b. 3/8 c. 1/2 d Tommy estimates that the probability of his passing Chemistry or English is 0.8, the probability of his passing Chemistry is 0.7, but his probability of passing both is 0.5. What should be his estimate of the probability of his passing English? a. 0.3 b. 0.4 c. 0.5 d. 0.6 e Two cards are drawn in succession and without replacement from a standard deck of 52 cards. The probability that they are both red face cards (Jack, Queen, King) is a b c d. ( 3 13 )2
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