hw2 - ORIE 3500/5500 Engineering Probability and Statistics...

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ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 2 Problem 1 A set of k coupons, each of which is independently a type j coupon with probability p j , n j =1 p j = 1, is collected. Find the probability that the set contains a type i coupon but not any type j coupons. Problem 2 Let A , B , C be events such that P ( A ) = . 7, P ( B ) = . 6, P ( C ) = . 8. Find the probability that at least one of the events A and B occurs if ( a ) A c and B are mutually exclusive; ( b ) A c and B are independent. Find the probability that all of the events A , B and C occur if ( c ) A c , B c and C c are independent; ( d ) A c , B c and C c are mutually exclusive. Problem 3 Suppose that distinct numbers are written on each of 3 cards. Suppose you are to be offered these cards in random order. When you are offered a card, you must immediately either accept it or reject it. If you accept a card, the process ends. If you reject a card, then the next card (if there is one) is offered. If you you reject the first two cards, you have to accept the final card.
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