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midterm 2003 - 3 There are 3 coins in a box One is a...

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Statistics 116 Midterm Examination - July 19-9:OOa.m NAME: Show all work! Justify your assertions! 1. An urn contains n white and m black balls, where m and n are positive integers. a. If 2 balls are randomly withdrawn (without replacement), what is the probability that they are the same color? (10 points) b. If a ball is randomly withdrawn and then replaced before the second one is drawn, what is the probability that the withdrawn balls are the same color? (10) 2. A pediatrician wishes to recruit 5 couples, each of whom is expecting their first child, to participate in a new natural childbirth regimen. If p = .2 is the probability that a randomly selected couple agrees to participate, what is the probability that exactly 15 couples must be asked before 5 are found who agree to participate? (20)
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Unformatted text preview: 3. There are 3 coins in a box. One is a two-headed; another is a fair coin; and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin? (20) 4. Suppose only 40% of all drivers in a certain state regularly wear a seatbelt. A random sample of 500 drivers is selected. What is the approximate probability that between 180 and 230(inclusive) of the drivers in the sample regularly wear a seatbelt? (20) 5. A coin that when flipped comes up heads with probability p. Let X be the number of flips required until either heads or tails has occurred twice. Find the probability mass function of X. Find the expectation of X. (20)...
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