# 180ahw2 - MATH 180A Introduction to Probability Homework...

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MATH 180A – Introduction to Probability Homework 2 (due 10/09/06) 1. After asking many individuals across the nation, a researcher comes with the following conclusion: 65% like dogs 55% like cats 25% like both (a) What is the proportion of people that like neither? (b) What is the proportion of people that like exactly one? (c) What is the proportion of people that like at least one? (d) What is the proportion of people that like at most one? (e) What is the proportion of people that like exactly one among those that like at least one? (f) What is the proportion of people that like both among those that like at least one? (g) What is the proportion of people that do not like cats among those that like dogs? 2. Two fair dice are rolled. What is the probability that the number on the first die was at least as large as 4 given that the sum of the two dice was eight? 3. An urn contains two red balls and four blue balls. A ball is chosen (uniformly) at
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