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ec41f10FIN_sol

# ec41f10FIN_sol - Kata Bognar [email protected] Economics 41...

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Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Fall 2010 Final Exam - suggested solutions - Part I - Multiple Choice Questions (4 points each) 1. Two unbiased four-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is 3? D (a) 1/16 (b) 3/16 (c) 4/16 (d) none of the above Explanation: The sum of the numbers on the two dice is 3 if the first die shows 1 and the second shows 2 or if the first die shows 2 and the second shows 1. These outcomes happen with probability 1/16, each, so the probability of the event above is 2/16. 2. Suppose that A and B are events and P ( B ) = 0 . 6, P ( A | B ) = 0 . 5, then P ( B | A ) = D 3. At a grocery store, eggs come in cartons that hold a dozen eggs. Experience indicates that 76% of the carton have no broken eggs, 20% have one broken egg, 3% have two broken eggs and 1% have three or more broken eggs. An egg selected random from a cartoon and is found to be broken. What is the probability that this is the only broken egg in the carton? C 4. Two events are said to be independent if the occurrence of one event: B 5. Let X denote the number of corporations in a random sample of 4 that provide retirement benefits. Assume that the population consists of 16 corporations, of which 3 provide retirement benefits. Then X is a hypergeometric random variable with N = 16 , r = 3 , and n = 4 . The probability that at most one of the selected firms offers retirement benefits is: A 1

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(a) 0.8643 (b) 0.7711 (c) 0.1357 (d) 4091 Explanation: By the hypergeometric probability formula, P ( X = x ) = ( 13 4 - x )( 3 x ) ( 16 4 ) . Then the probability P ( X 1) = P ( X = 0) + P ( X = 1) = ( 13 4 )( 3 0 ) ( 16 4 ) + ( 13 3 )( 3 1 ) ( 16 4 ) = 0 . 8643 .
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