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# homework2 - color is 0.44 Calculate the number of blue...

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STAT 34500/51100 STATISTICS SPRING 2011 Homework 2 Date : February 10, 2011. Name: Due : February 17, 2011 PUID: Q.N. 1) Let A and B be two events such that P ( A B ) = 0 . 7 and P ( A B c ) = 0 . 9 Find p ( A ) . Q.N. 2) A garage door opener has 6 toggle switches, each with three settings: up, center and down. a) In how many ways can these switches be set? b) If a thief knows the type of the opener involved but does not know the setting what is the probability that he/ she can guess the setting on the first attempt? c) How many settings are possible in which two switches are up, two are down and two are in center? Q.N. 3) An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same
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Unformatted text preview: color is 0.44 . Calculate the number of blue balls in the second urn? Q.N.4) Suppose A and B are two independent events. Prove that A c and B c are also independent. Note that A c and B c denotes the complements of A and B respectively. Q.N. 5) A total of 46 percent of the voters in a certain city classify themselves as Independents, whereas 30 percent classify themselves as Liberals and 24 percent as Conservatives. In a recent local election, 35 percent of the Independents, 62 percent of the Liberals, and 58 percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he/she is a) an Independent? b) a Liberal? c) a Conservative? [Hint: Use Bayes’ Theorem] 1...
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