lecture02-sep10

lecture02-sep10 - STAT 430 Probability Lecture 2 Fall, 2007...

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STAT 430 Probability Lecture 2 Fall, 2007
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Homework HW1 (Due in Class on Monday, September 17): Section 1.1: 2, 3*, 5*, 6; Section 1.3: 2*, 4, 6, 8, 13*, 14*, 15*. Problems with * are suggested exercises. These problems are not graded.
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Properties of Probability For any event A , P( A c ) = 1 - P( A ). If A B , then P( A ) P( B ). For any two events A and B , P( A B ) = P( A ) + P( B ) - P( A B ). For three events, A , B , and C , P( A B C ) = P( A ) + P( B ) + P( C ) - P( A B ) - P( A C ) - P( B C ) + P( A B C ).
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Properties of Probability If A 1 , A 2 , … A n is a partition of A , then P(A) = P( A 1 ) + P( A 2 ) + ...+ P( A n ) ( A 1 , A 2 , … A n is called a partition of A if A 1 A 2 A n = A and A 1 , A 2 , … A n are mutually exclusive.)
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Example A diagnostic test for the AIDS virus has probability of .005 of producing a false positive. If the 140 employees of a medical clinic are tested and all are free of AIDS, what is the probability that at least one false positive will occur? It’s reasonable to assume that the test results for
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lecture02-sep10 - STAT 430 Probability Lecture 2 Fall, 2007...

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