hmwk4 - ISyE 2027 Probability with Applications Fall 2006 R...

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Unformatted text preview: ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 4 September 13, 2006 due on Tuesday, 19 September 1. Suppose we have a sample space with Pr( A ) = . 4, Pr( B ) = . 3, and Pr( A ∪ B ) = . 5. Compute (a) Pr( B | A ), (b) Pr( A | B ), (c) Pr( ¯ A | B ), and (d) Pr( A | ¯ B ). (e) Are A and B independent? 2. Suppose you are dealt 6 cards from a well-shuffled standard deck. (a) What is the probability of having 3 pairs? (b) What is the probability of having 3 pairs with one pair being aces? (c) What is the probability of having 3 aces and 1 pair? (d) What is the probability of having a six card straight assuming the ace can only be high? (e) What is the probability of being dealt a six card flush in hearts given that all six cards are red? 3. For a well-shuffled deck of cards, compute the following: (a) What is the probability that the top two cards are red given that the top card is red? (b) What is the probability that the top two cards are red given that at least one of the top two cards is red?red given that at least one of the top two cards is red?...
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