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HW9Answers(3.3) - i(note that M i is a partition of the...

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Math331, Spring 2008 Instructor: David Anderson Section 3.3 Homework Answers Homework: pgs. 96-97 #’s 1, 7, 9, 13. 1. Let A be the event that a given person is colorblind. Let M be the event that a person is male. Then, assuming that half the population is male, P ( A ) = P ( A | M ) P ( M ) + P ( A | M c ) P ( M c ) = . 05 * 1 / 2 + . 0025 * 1 / 2 = 0 . 02625 . 7. Let A be the event that a person tells the truth and let B be the event that a person is under 45 years of age. Then, P ( A ) = P ( A | B ) P ( B ) + P ( A | B c ) P ( B c ) = . 65 * . 63 + . 8 * . 37 = 0 . 7055 . 9. Let D be the event that a single piece of whatever this factory makes is defective. Let M i represent the event that a single output item was manufactured by machine
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Unformatted text preview: i (note that M i is a partition of the sample space S = { ( x,y ) | x ∈ { Defective , non-defective } ,y ∈ { Mach 1 , Mach 2 , Mach 3 }} ). Then, P ( D ) = 3 s i =1 P ( D | M i ) P ( M i ) = . 04 * . 5 + . 02 * . 3 + . 04 * . 2 = 0 . 034 . 13. Let W be the event the child is lost in the west wing and W c be the event that the child is lost in the east wing. Let F be the event that the child is found. Then, P ( F ) = P ( F | W ) P ( W ) + P ( F | W c ) P ( W c ) = . 4 * . 75 + . 4 * . 25 = . 4 1...
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