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At Least One Problems, Prof. Landesman 1. The probability is ¾ that a pea pod is green. Otherwise it is yellow. Four pea pods are picked at random. a) Find the probability that all are yellow. b) Find the probability that at least 1 is green. c) Find the probability that all are green. d) Find the probability that at least 1 is yellow. e) Find the probability that exactly 3 are green. f) Find the probability that at least 3 are green. g) Find the probability that at most 1 is yellow. 2, Based on a Harris Interactive poll, 20% of adults believe in reincarnation. Assume that three adults are randomly selected, and find the indicated probability. a. What is the probability that at least one of the selected adults believe in reincarnation? b. What is the probability that at least one of the selected adults does not believe in reincarnation? c. What is the probability that at most 2 of the selected adults believe in reincarnation? d. What is the probability that at most 2 of the selected adults do not believe in reincarnation? e. What is the probability that exactly 2 of the selected adults believe in reincarnation? f. What is the probability that at least 2 of the selected adults believe in reincarnation? g. What is the probability that at most of the selected adults believe in reincarnation? 3. A basketball player take a free though shot with the probability 1/4 of successfully making the basket. He takes 5 shots. a. What is the probability that all 5 shots will go in? b. What is the probability that none will go in? c. What is the probability that at least 1 will go in? d. What is the probability that at most 4 will go in? E. What is the probability that exactly 3 will go in? F. What is the probability that exactly 2 will go in? G. What is the probability that at least 4 will go in? 4. Assume that boys and girls are equally likely. What is the probability that out of six births 3 are boys? Answers to second page problems: 5a. 9999/10000 5b. 3439/10000 5c. 3439/10000 5d. 9999/10000 6a.76479/160000 6b.159919/160000 6c.81/160000 6d. 76479/160000 7a. 32/3125 7b.2884/3125 7c.3093/3125 7d.2884/3125

5. Tainted Currency Based on the American Chemical Society, there is a 9/10 probability that in the United States, a randomly selected dollar bill is tainted with traces of cocaine. Assume that four dollar bills are randomly selected. a. What is the probability that at least one of the selected dollar bills is tainted with traces of cocaine? b. What is the probability that at least one of the selected dollar bills is not tainted with traces of cocaine? c. What is the probability that at most 3 of the selected dollar bills is tainted with traces of cocaine? d. What is the probability that at most 3 of the selected dollar bills is not tainted with traces of cocaine? e. Find the probability that at most 1 have traces of cocaine. f. Find the probability that at exactly 3 of them have traces of cocaine. g. Find the probability that at least 3 of them have traces of cocaine 6. Car Crashes The probability of a randomly selected car crashing during a year is 3/20 (based on data from the Statistical Abstract of the United States ). If a family has 4 cars, find the probability that at least one of them has a crash during the year. a. What is the probability that at least one of the cars will crash? b. What is the probability that at least one of the at least one of cars will not crash? c. What is the probability that at most 3 of the cars will crash? d. What is the probability that at most 3 of the cars will not crash? e. What is the probability that exactly 2 of the cars will crash? f .What is the probability that at most1 of the cars will crash? g. What is the probability that at least 3 of the cars will crash? 7. A basketball player take a free though shot with the probability 2/5 of successfully making the basket. He takes 5 shots. a. What is the probability that all 5 shots will go in? b. What is the probability that at least 1 will go in? c. What is the probability that at least 1 will not go in? d. What is the probability that at most 4 will go in? E. What is the probability that exactly 4 will go in? F. What is the probability that exactly 3 will go in? G. What is the probability that at least 4 will go in? Answers for first page,1a. 1/256 1b. 255/256 1c. 81/256 1d.175/256 2a.61/125 2b.124/125 2c.624/625 2d.13/25 3a. 1/1024 3b. 243/1024 3c. 781/1024 3d. 1023/1024 4. 5/16

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