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midterm-solutions - Problem 1 Sample space S =cfw_all...

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Problem 1. Sample space S = { all possible combinations of the two teams that can be formed } . | S | = 10 5 · 15 5 . We assume all possible team combinations are equally likely. 1. Define E = { teams chosen such that Lebron is on company A’s team AND Larry is on company B’s team } . We want to find P ( E ) and we know that P ( E ) = | E | | S | . A team for company A with Lebron in it can be chosen ( 9 4 ) ways. A team for company B with Larry in it can be chosen ( 14 4 ) ways. So | E | = 9 4 · 14 4 . Therefore P ( E ) = | E | | S | = ( 9 4 ) · ( 14 4 ) ( 10 5 ) · ( 15 5 ) . = 1 6 = . 167 . 2. Define F = { teams chosen such that Lebron does not play and Larry does play for company B } . We want P ( F ). A team for company A with Lebron not playing can be chosen ( 9 5 ) ways. A team for company B with Larry playing in it can be chosen ( 14 4 ) ways (as before). Then | F | = 9 5 · 14 4 . Therefore P ( E ) = | F | | S | = ( 9 5 ) · ( 14 4 ) ( 10 5 ) · ( 15 5 ) . = 1 6 = . 167 . Problem 2. Define F i = { firm i is involved } , i = 1 , 2 , 3 , C = { a cost overrun occurs } . We are given P ( F 1 ) = . 5 , P ( F 2 ) = . 2 . P ( C | F 1 ) = . 05 , P ( C | F 2 ) = . 1 , P ( C | F 3 ) = . 15 .
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