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Unformatted text preview: SIEO 3600 (IEOR Majors) Solution to Practice Problem Set #1 Introduction to Probability and Statistics February 16, 2010 Solution to Practice Problem Set #1 1. Five independent flips of a fair coin are made. Find the probability that (a) the first three flips are the same; (b) either the first three flips are the same, or the last three flips are the same; (c) there are at least two heads among the first three flips, and at least two tails among the last three flips. Solution: (a) P ( first three are the same ) = P ( first three are H’s) + P ( first three are T’s) = (1 / 2) 3 + (1 / 2) 3 = 1 / 4. (b) Let L 3 ≡ { last three are the same } , let F 3 ≡ { first three are the same } . Then P ( L 3 ) = P ( F 3 ) = 1 / 4. P ( L 3 ∩ F 3 ) = P (all five are the same) = (1 / 2) 5 · 2 = 1 / 16. Therefore, P ( L 3 ∪ F 3 ) = P ( L 3 ) + P ( F 3 ) P ( L 3 ∩ F 3 ) = 1 / 4 + 1 / 4 1 / 16 = 7 / 16. (c) Enumerate all possible outcomes: ( H,H,H,T,T ), ( H,H,T,T,T ), ( H,H,T,H,T ), ( H,H,T,T,H ), ( H,T,H,T,T ), (...
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This note was uploaded on 10/03/2011 for the course SIEO W3600 taught by Professor Yunanliu during the Spring '10 term at Columbia.
 Spring '10
 YUNANLIU

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