Hw2sol - ISyE 2027B Probability with Applications Fall 2010...

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Unformatted text preview: ISyE 2027B Probability with Applications Fall 2010 Homework 2 Solutions Q1. (a) 10 points There are ( 7 2 ) + ( 6 2 ) + ( 9 2 ) ways of getting a pair out of the total of (7+6+9) socks. Hence the probability of getting a pair by randomly drawing two socks in the dark equals ( 7 2 ) + ( 6 2 ) + ( 9 2 ) ( 22 2 ) = 24 77 (b) 10 points There are ( 7 2 ) ways of getting a white pair. The probability of getting a white pair equals ( 7 2 ) ( 22 2 ) = 1 11 Q2. 20 points Let g,s be the outcomes that correspond to a gold or silver coin is found in any opened drawer. Ω = { ( g,g ) , ( g,s ) , ( s,g ) , ( s,s ) } , each element of which corresponds to the two coins found in the chosen cabinet. P (the other = s | the first one = s ) = P (( s,s ) |{ ( s,g ) , ( s,s ) } ) = P (( s,s )) P ( { ( s,g ) , ( s,s ) } ) = P (Cabinet C is chosen) P ( { Cabinet B is chosen and the first coin = s } ∪ { Cabinet C is chosen } ) = 1 3 1 3 × 1 2 + 1 3 = 2 3 Q3. 20 points Define the events R 1 and R 2 as: a red ball is drawn on the first and the...
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This note was uploaded on 02/21/2011 for the course ISYE 2027 taught by Professor Zahrn during the Fall '08 term at Georgia Tech.

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Hw2sol - ISyE 2027B Probability with Applications Fall 2010...

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