Prelim I Solutions

Prelim I Solutions - ENGRD 2700, Spring’09 Prelim 1...

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Unformatted text preview: ENGRD 2700, Spring’09 Prelim 1 Solutions Prelim 1 Solutions Feb 19, 2009 Solution to Problem 1. Let us define the events D := The building gets an award for its design E := The building gets an award for environmental efficiency We are given that P ( D ) = 0 . 16 P ( E ) = 0 . 24 P ( D ∩ E ) = 0 . 11 (a) The required probability is P ( D ∪ E ) = P ( D ) + P ( E )- P ( D ∩ E ) = 0 . 16 + 0 . 24- . 11 = 0 . 29 (b) The required probability is P (( D ∩ E c ) ∪ ( E ∩ D c )) = P ( D ∩ E c ) + P ( E ∩ D c ) = { P ( D )- P ( D ∩ E ) } + { P ( E )- P ( D ∩ E ) } = P ( D ) + P ( E )- 2 P ( D ∩ E ) = 0 . 16 + 0 . 24- 2 × . 11 = 0 . 18 (c) The required probability is P ( D c ∩ E c ) = 1- P ( D ∪ E ) = 1- . 29 = 0 . 71 , where the first equality follows from the observation that D c ∩ E c is the complement of ( D ∪ E ). (d) Since P ( D ∩ E ) = 0 . 11 6 = ( . 24)( . 16) = 0 . 0384 = P ( D ) P ( E ) , it follows that D and E are not independent....
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This note was uploaded on 10/29/2011 for the course ENGRD 270 taught by Professor Resnick during the Spring '07 term at Cornell.

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Prelim I Solutions - ENGRD 2700, Spring’09 Prelim 1...

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