5500SOL2 - ORIE 3500/5500 Fall Term 2008 Assignment...

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ORIE 3500/5500 Fall Term 2008 Assignment 2-Solution 1. Let A 1 ,A 2 and A 3 be the events that first, second and third friend hit the deer respectively. They are independent and P ( A 1 ) = 0 . 3 ,P ( A 2 ) = 0 . 4 ,P ( A 3 ) = 0 . 5 . (a) P ( A 1 A 2 A 3 ) = P ( A 1 ) P ( A 2 ) P ( A 3 ) = 0 . 3 × 0 . 4 × 0 . 5 = 0 . 06 . (b) The required probability is P ( A 1 A 2 A c 3 ) + P ( A 1 A c 2 A 3 ) + P ( A c 1 A 2 A 3 ) = P ( A 1 ) P ( A 2 ) P ( A c 3 ) + P ( A 1 ) P ( A c 2 ) P ( A 3 ) + P ( A c 1 ) P ( A 2 ) P ( A 3 ) = 0 . 3 × 0 . 4 × (1 - 0 . 5) + 0 . 3 × (1 - 0 . 4) × 0 . 5 + (1 - 0 . 3) × 0 . 4 × 0 . 5 = 0 . 06 + 0 . 09 + 0 . 14 = 0 . 29 (c) Let F be the event that exactly one bullet hit the deer. Then F = ( A 1 A c 2 A c 3 ) ( A c 1 A 2 A c 3 ) ( A c 1 A c 2 A 3 ) and P ( F ) = P ( A 1 A c 2 A c 3 ) + P ( A c 1 A 2 A c 3 ) + P ( A c 1 A c 2 A 3 ) = P ( A 1 ) P ( A c 2 ) P ( A c 3 ) + P ( A c 1 ) P ( A 2 ) P ( A
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5500SOL2 - ORIE 3500/5500 Fall Term 2008 Assignment...

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