# 01_28 - STAT 400 Examples for Spring 2011 Events A and B...

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Examples for 01/28/2011 Spring 2011 Events A and B are independent if and only if P ( B A ) = P ( B ) P ( A B ) = P ( A ) P ( A B ) = P ( A ) P ( B ) 1. The probability that a randomly selected student at Anytown College owns a bicycle is 0.55, the probability that a student owns a car is 0.30, and the probability that a student owns both is 0.10. Are events {a student owns a bicycle} and {a student owns a car} independent? Events A, B and C are independent if and only if P ( A B ) = P ( A ) P ( B ), P ( A C ) = P ( A ) P ( C ), P ( B C ) = P ( B ) P ( C ), and P ( A B C ) = P ( A ) P ( B ) P ( C ) 2. A girl is told by her boyfriend that she is “one in a billion.” She has a dimple in her chin, probability 1 / 100 , eyes of different colors, probability 1 1,000 , and is absolutely crazy about mathematics, probability 1 10,000 b) Show why the girl is “one in a billion.”

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## This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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01_28 - STAT 400 Examples for Spring 2011 Events A and B...

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