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ex_0 - Introduction to Information Theory(67548 Assignment...

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Introduction to Information Theory (67548) November 10, 2008 Assignment 0: Probability Review Lecturer: Prof. Michael Werman Due: Sunday, Nov. 16, 2008 Problem 1 Probability and Conditional Probability Suppose that in all families with two children, all four combinations of boy-boy, boy-girl, girl-boy, and girl-girl are equally probable. Part (a) Given that a family with two children has at least one boy, what is the probability that it also has a girl? Part (b) Suppose that one visits at random a family with two children, and a boy opens the door and says (truthfully) ‘I am the ﬁrst child’. What is the probability that he has a sister? Suppose the boy says ‘I am the second child’ instead. What is the probability that he has a sister? Part (c) Suppose the boy opens the door and says nothing. What is the probability that he has a sister? Why is the answer diﬀerent from either Part (a) or Part (b)? Problem 2

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ex_0 - Introduction to Information Theory(67548 Assignment...

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