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HW 3 Solutions - Steven Weber Dept of ECE Drexel University...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Homework 3 Solutions Question 1: Exercise 55, § 2.4, p75. Deer ticks can be carriers of either Lyme disease or human granulo- cytic ehrlichiosis (HGE). Based on a recent study, suppose that 16% of all ticks in a certain location carry Lyme disease, 10% carry HGE, and 10% of the ticks that carry at least one of these diseases in fact carry both of them. If a randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier of Lyme disease? Let A = carries Lyme disease and B = carries HGE. We are told P ( A ) = 0 . 16, and P ( B ) = 0 . 10, and P ( A B | A B ) = 0 . 10. Then: 0 . 1 = P ( A B | A B ) = P (( A B ) ( A B )) P ( A B ) = P ( A B ) P ( A B ) . (1) Next: P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = P ( A ) + P ( B ) - 0 . 1 P ( A B ) . (2) Solving this equation yields P ( A B ) = 0 . 236364. Now use P ( A B ) = 0 . 1 P ( A B ) = 0 . 02364. Next use P ( A | B ) = P ( A B ) P ( B ) = 0 . 02364 / 0 . 1 = 0 . 2364.
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