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# hw7 - A,B(a if p A p B> 1 then p A ∩ B> 0(b If p...

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ECE 103 Discrete Math for Engineers University of Waterloo Spring 2010 Instructors: Koray Karabina, Ashwin Nayak Homework 7, due July 12, 2010 Question 1. [8 marks] Problem 37, page 133 of the text book. Question 2. [7 marks] Consider families with three children. Are the events E , that a family has children of both sexes, and F , that a family has at most one boy, independent? Are the events E and F independent if we consider families with four children? Assume that each child is equally likely to be a boy or a girl, so that all the 2 n ways in which a family can have n children are equally likely. Question 3. [4 marks] Prove that for any two events
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Unformatted text preview: A,B : (a) if p ( A ) + p ( B ) > 1, then p ( A ∩ B ) > 0. (b) If p ( A ) > ,p ( B ) > 0, and p ( A | B ) > p ( A ), then p ( B | A ) > p ( B ). Question 4. [6 marks] I have three 1 cent coins, one of which is a counterfeit. The counterfeit coin turns up leaf 60% of the times when tossed, whereas the other two are fair coins (they turn up leaf 50% of the times). I pick one of the three coins at random, and toss it twice. I get one leaf and one queen, in that order. What is the probability that I picked the counterfeit coin? 1...
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