Solution for Hw1 of Dr. Zou

Solution for Hw1 of Dr. Zou - CDA5530 Performance Models of...

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CDA5530: Performance Models of Computers and Networks (Fall 2009) Homework 1 Solution 1. Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with prob. 0.7, George, independently, hits the target with prob. 0.4. a). Now both of them shoot once and exactly one shot hits the target. What is the prob. that it was George's shot? Solution : The first step is modeling. For this question, it is about how to define suitable “events”. B: Bill shoots a target P(B) = 0.7 G: George shoots a target P(G)=0.4 E: event of “both of them shoot once and the target was hit once” Question a) asks us to calculate P(G|E) From conditional probability formula: P(G|E) = P(GE)/P(E) P(GE) = P(“George hits the target and Bill misses”) = P(G)*[1-P(B)] = 0.4*0.3 = 0.12 P(E) = P(G)[1-P(B)] + [1-P(G)]P(B) = 0.4*0.3 + 0.6*0.7 = 0.54 Therefore, P(G|E) = 0.12/0.54 = 0.22 b). Now both of them shoot once and the target is hit. What is the prob. that George hit it? Solution : E: event of “the target is hit”, which means the target is hit either once or twice. P(E) = 1 – P(E c ) =1- P(“no one hits the target”) =1- [1-P(B)] * [1-P(G)] =1- 0.3*0.6 = 0.82 P(GE) = P(G) = 0.4 The question asks us to calculate P(G|E): P(G|E) = P(GE)/P(E) = 0.4 / 0.82 = 0.49 2. A gamber has in his pocket a fair coin and a two-headed coin. He selects one of the coins at a random, and when he flips it, it shows heads. a). What is the probability that it is a fair coin?
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This note was uploaded on 10/15/2009 for the course CS 5530 taught by Professor Zou during the Fall '09 term at Central State University.

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Solution for Hw1 of Dr. Zou - CDA5530 Performance Models of...

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