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 boyboy, boygirl, girlboy, and
girlgirl 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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 Spring '08
 MichaelWerman
 Probability, Probability theory, ProbabiliTy Review

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