A maintenance firm has gathered the following information regarding the failure mechanism for air conditioning systems. Gas Leaks Yes Evidence of Yes 63 electrical failure No 25 No 18 21 If this is a representative sample of AC failure, find the following probabilities. (a) That there was evidence of electrical failure, given that there was a gas leak. (b) That there was a gas leak, given that there was evidence of electrical failure. (c) Let E be the event that there is a gas leak and let F be the event that there is evidence of electrical failure. Find P(FCE).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A maintenance firm has gathered the following information regarding the failure mechanism for air conditioning
systems.
Gas Leaks
Yes
Evidence of
Yes
63
electrical failure No 25
No
18
21
If this is a representative sample of AC failure, find the following probabilities.
(a) That there was evidence of electrical failure, given that there was a gas leak.
(b) That there was a gas leak, given that there was evidence of electrical failure.
(c) Let E be the event that there is a gas leak and let F be the event that there is evidence of electrical failure.
Find P(FCE).
Transcribed Image Text:A maintenance firm has gathered the following information regarding the failure mechanism for air conditioning systems. Gas Leaks Yes Evidence of Yes 63 electrical failure No 25 No 18 21 If this is a representative sample of AC failure, find the following probabilities. (a) That there was evidence of electrical failure, given that there was a gas leak. (b) That there was a gas leak, given that there was evidence of electrical failure. (c) Let E be the event that there is a gas leak and let F be the event that there is evidence of electrical failure. Find P(FCE).
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