winter 2007 STAT 230 test07W-3-soln

winter 2007 STAT 230 test07W-3-soln - STAT 230 Test 3 Feb...

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STAT 230 Test 3 Feb 14, 2007 3:30 pm 4:10 pm ______________________________________________________________________ 1. At the beginning of a computer game, Tom is given 5 different weapons to hit a target. The probability that Tom hits the target with any of these weapons is 0.7, independent among different plays. He uses each weapon 3 times and he can keep the weapon if he hits the target at least twice; otherwise the weapon is lost. [4] (a) For a selected weapon, show that P ( Tom will lose it) = 0.216. 216 . ) 3 (. ) 7 (. 1 3 ) 3 (. ) 7 (. 0 3 ) 1 ( ) 7 ,. 3 ( ~ 2 1 3 0 = + = X P Bi X [4] (b) Find the probability that Tom will keep 4 or more weapons after he used all five weapons. (You can use the result given in (a) if needed, same below for (c)). 0 5 1 4 ) 216 (. ) 784 (. 5 5 ) 216 (. ) 784 (. 4 5 ) 4 ( ) 784 ,. 5 ( ~ + = X P Bi X [4] (c) If we know that Tom hit the target a total of 4 times after using the first two weapons (he tried each weapon 3 times), what is the probability that he lost the first weapon? Let X be the number of hits of the first weapon; Y the second weapon. 5 1 3 . 7 . 1 3 3 . 7 . 3 3 3 . 7 . 2 3 3 . 7 . 2 3 3 . 7 . 3 3 3 . 7 . 1 3 3 . 7 . 3 3 3 . 7 . 1 3 3 . 7 . 4 6 3 . 7 . 3 3 3 . 7 . 1
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winter 2007 STAT 230 test07W-3-soln - STAT 230 Test 3 Feb...

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