20082ee131A_1_HW3

# 20082ee131A_1_HW3 - EE 131A Homework #3 Due April 23rd Read...

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EE 131A Homework #3 Spring 2008 Due April 23rd K. Yao Read Leon-Garcia (3rd edition), pp. 97–104; 141-146. 1. A batch of 500 containers of frozen orange juice contains 5 that are defective. Two are selected randomly one after the other without replacement. a. What is the probability that the second one selected is defective given that the ﬁrst one was defective? b. What is the probability that both are defective? c. What is the probability that both are non-defective? 2. In the above problem, let A and B denote the events that the ﬁrst and second container selected is defective, respectively. a. Are A and B independent events? b If the sampling were done with replacement, would A and B be independent? 3. Use the fact P ( D E ) = P ( D )+ P ( E ) - P ( D E ) and standard rules of set operations to prove P ( A B C ) = P ( A ) + P ( B ) + P ( C ) - P ( A B ) - P ( A C ) - P ( B C ) + P ( A B C ) . 4. A number

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## This note was uploaded on 04/12/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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20082ee131A_1_HW3 - EE 131A Homework #3 Due April 23rd Read...

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