sample_midterm_solution

# sample_midterm_solution - IEOR 172 SAMPLE MIDTERM SOLUTIONS...

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IEOR 172 SAMPLE MIDTERM SOLUTIONS Problems 1) 150 * 0 . 7 = 105 males smoke cigarettes. Therefore 140 - 105 = 35 females smoke cigarettes. a.) P ( F S c ) = P ( F )+ P ( S c ) - P ( F S c ) = (100 / 250)+(110 / 250) - (65 / 250) = 145 / 250. b.) P ( S c | F ) = P ( F S c ) P ( F ) = 65 100 c.) P ( S F ) = 35 / 250 6 = (100 / 250)(140 / 250) = P ( F ) P ( S ). Therefore they are not independent. 2.) P ( AB ) = 0. Since they are mutually exclusive they can not happen together. 3.) Let M be the event that a person suﬀers from Methusaleh syndrome and let P be the event that test result is positive. a.) P ( M | P ) = P ( P | M ) P ( M ) P ( P | M ) P ( M )+ P ( P | M c ) P ( M c ) = 0 . 99(0 . 05) 0 . 99(0 . 05)+0 . 04(0 . 95) = 0 . 57 b.) P ( P ) = P ( P | M ) P ( M ) + P ( P | M c ) P ( M c ) = 0 . 0875 P ( P M ) = P ( P | M ) P ( M ) = 0 . 99(0 . 05) = 0 . 0495 P ( P M ) = ( P ) + P ( M ) - P ( P M ) = 0 . 0875 + 0 . 05 - 0 . 0495 = 0 . 538 c.)Let P i be the events that a person tests positive on test

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## This note was uploaded on 02/10/2010 for the course IEOR 160 taught by Professor Hochbaum during the Spring '07 term at Berkeley.

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sample_midterm_solution - IEOR 172 SAMPLE MIDTERM SOLUTIONS...

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