3. A maintenance firm has gathered the following information regarding the failu

Question

3. A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning systems Evidence of gas leaks Yes Evidence of electrical failure Yes No No 17 32 The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability (a) That failure involves a gas leak (b) That there is evidence of electrical failure given that there was a gas leak (c) That there is evidence of a gas leak given that there is evidence of electrical failure

Explanation / Answer

Question 3

(a) Pr(failure involves gas leak) = (55 + 32)/ (55 + 32 + 17 + 3) = 87/107 = 0.813

(b) Pr(Electical failure l Gas leak) = 55/(55 + 32) = 55/87 = 0.632

(c) Pr(Gas leak l Electical failure) = 55/(55 + 17) = 55/72 = 0.764

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