Sol III - ENGM2032, Applied Probability and Statistics...

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Unformatted text preview: ENGM2032, Applied Probability and Statistics Winter 2010 Assignment #3: Solutions 1) Let S be the event that the company sells its products online. Let H be the event that the company experiences at least one hacking attack a day. We are given: P S = 0 . 70, P H j S = 0 . 80, P H j S c = 0 . 15, so that we can construct the following probability tree, S S H H H H 0.70 0.30 0.80 0.15 0.20 0.85 c c c a) P H = P H j S P S + P H j S c P S c = (0 . 80)(0 . 70) + (0 . 15)(0 . 30) = 0 . 605 . b) P S j H = P H j S P S P H = (0 . 8)(0 . 7) . 605 = 0 . 9256 . 2) Let A be the event that the symbol is letter a. Let R be the event that the symbol is recognized as letter a. We are given: P A = 86 / 1000 = 0 . 086, P R c j A = 60 / 1000 = 0 . 06, and P R j A c = 47 / 1000 = 0 . 047. Then, we can construct a probability tree for this problem, A A R R R R 0.086 0.914 0.94 0.047 0.06 0.953 c c c a) P R = P R j A P A + P R j A c P A c = (0 . 94)(0 . 086) + (0 . 047)(0 . 914) = 0 . 1238 . b) P A j R = P R j A P A P R = (0 . 94)(0 . 086) . 1238 = 0 . 653 . c) P A c j R = P R j A c P A c P R = (0 . 047)(0 . 914) . 1238 = 0 . 347 . 3) Let R be the event that the temperature rises above 30 o C during the day. Let A be the event that the air conditioning system malfunctions during the day. Let S be the event that there is a problem with at least one of the servers during the day....
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This note was uploaded on 02/24/2010 for the course ENGM 2032 taught by Professor Yao during the Spring '10 term at Dalhousie.

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Sol III - ENGM2032, Applied Probability and Statistics...

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