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131A_1_hw2

# 131A_1_hw2 - a question given that he or she answered it...

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EE 131A Problem Set #2 Probabilities Wednesday, October 12, 2005 Instructor: Vwani Roychowdhury Due: Wednesday, October 19, 2005 1. Problem 2.57 2. Problem 2.59 3. Problem 2.61 4. A familily has two children, assuming that one of them is a girl what is the probability that the other child is also a girl, given that a boy and girl are equiprobable. 5. (a) Show that if the events S 1 , S 2 , ..., S n are mutually exclusive and L = S 1 S 2 · · · S n , then P ( A | L ) = n k =1 P ( A | S k ) P ( S k ) P ( L ) (1) (b) Form the above follows that if P ( A | S i ) = P ( B | S i ) i = 1 , 2 , · · · , n (2) then P ( A | L ) = P ( B | L ) (3) Is this conclusion true if the events S i , are not mutually exclusive? 6. In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let p be the probability that the student knows the answer and 1 - p the probability that the student guesses. Assume that a student who guesses at the 1

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answer will be correct with probability 1 /m , where m is the number of multiple-choice alternatives. Whats the conditional probability that a student knew the answer to
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Unformatted text preview: a question, given that he or she answered it correctly? Give the numerical result if m = 5, p = 0 . 5. 7. Stores A , B , and C have 50, 75, and 100 employees and, repectively, 50, 60, and 70 percent of these are women. Resignations are euqally likely among all employees, regardless of sex. One employee resigns, and this is a women. What is the probability that she works in store C? 8. (a) A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the coins at random; when he ﬂips it, it shows heads. What is the probability that it is the fair coin? (b) Suppose that he ﬂips the same coin a second time and again it shows heads. What is now the probability that it is the fair coin? (c) Suppose that he ﬂips the same coin a third time and it shows tails. What is now the probability that it is the fair coin? 2...
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131A_1_hw2 - a question given that he or she answered it...

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