Seventy percent of people who hear worrisome noises in their automobiles wait mo

Question

Seventy percent of people who hear worrisome noises in their automobiles wait more than six weeks to visit a mechanic. Of those people who waited, 32% found that the original problem had caused another problem. Let's name events W: Waiting more than six weeks, and P2: A second problem was caused.

Referring to question 1, what is the probability that a second problem was caused, if a person waited more than six weeks to visit the mechanic? Enter your answer to three decimal places (0.XXX).?

Referring to question 1, what is the probability that a person waited too long to visit the mechanic, and a second problem was caused? Enter your answer to three decimal places (0.XXX).?

Explanation / Answer

Prob of waiting more than 6 weeks to visit mechanic:

P(W)=.7

Of those people who waited, 32% found that the original problem had caused another problem:

P(P2|W)=.32

prob of causing 2nd problem:

P(P2) = P(P2|W) * P(W) ............{from Bayes theorem}

P(P2) = .32*.7 = .224

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