Homework 6 - plane’s other engines. Furthermore, suppose...

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550.420 Introduction to Probability Fall 2011 Homework 7 Due October 13 [1] (2 points) Before having any children, a woman and her husband want to decide in advance how many children they will have. They want to have at least a 95% chance of having at least one boy and at least one girl. What is the minimum number of children that they should plan to have? [2] (2 points) If Paris Sheraton flips n+1 and Geneva Hilton flips n fair coins, find the probability that Paris gets more heads than Geneva. (Hint: Use conditioning. Reassurance: The answer may be somewhat surprising.) [3] (2 points) Suppose Professor Wierman often flies on DELTA (Don’t Expect Luggage To Arrive) airlines, and from experience finds that his luggage is lost 13% of the time. If he will fly on DELTA nineteen times during the year 2011, what is the most likely number of times that his luggage will be lost? [4] (2 points) Suppose that an aircraft engine will fail in flight with probability 1-p, independently of the
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Unformatted text preview: plane’s other engines. Furthermore, suppose that a plane can complete its flight successfully if at least half of its engines do not fail. (a) Is it true that a four-engine plane is always preferable to a two-engine plane? (that is, for all values of p) (b) Is it true that a five-engine plane is always preferable to a three-engine plane? [5] (2 points) A most amazing event occurred during the second round of the 1989 U.S. Open at Oak Hill in Pittsford, New York. Four golfers – Doug Weaver, Mark Wiebe, Jerry Pate, and Nick Price – made holes in one on the sixth hole. According to experts, the odds against a PGA golfer making a hole in one are 3708 to 1 – that is, the probability of making a hole in one is 1/3709. Approximate the probability that at least 4 of the 155 golfers playing in the second round would get a hole in one on the sixth hole that day....
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This note was uploaded on 02/26/2012 for the course STATISTICS 420 taught by Professor Wierman during the Fall '11 term at Johns Hopkins.

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