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5500HW1

5500HW1 - ORIE 3500/5500 Fall Term 2008 Assignment 1 Note...

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ORIE 3500/5500 Fall Term 2008 Assignment 1 Note that the due date is Monday September 15 at 1:00 pm you need to mention your section number on the top of your answer script. 1. [3 + 4 + 3 = 10 pts] Suppose A and B are two events. (a) If P ( A ) = 0 . 55, P ( B c ) = 0 . 35 and P ( A B ) = 0 . 75, then deter- mine P ( A B ) ,P ( A c B ) and P ( A B c ). (b) Show that ( A B ) ( A B ) c = ( A c B ) ( A B c ) . (c) Use part (b) to show that P (( A c B ) ( A B c )) = P ( A ) + P ( B ) - 2 P ( A B ) . 2. [2 + 2 + 2 = 6 pts] We roll a four-sided die and then we roll it as many times as is necessary to obtain a diﬀerent face than the one obtained in the ﬁrst roll. Let the outcome be ( r 1 ,r 2 ), where r 1 and r 2 are the results of the ﬁrst and last rolls respectively. Assume that all possible outcomes are equally likely. Find the probability that (a) r 1 is even. (b) Both

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5500HW1 - ORIE 3500/5500 Fall Term 2008 Assignment 1 Note...

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