My next-door neighbor George\'s car didn\'t start this morning. He was not sure

Question

My next-door neighbor George's car didn't start this morning. He was not sure if it was because of the battery or a damaged starter. If he replaces the battery, the engine will run with probability 0.8. If he replaces the starter, it will run with probability 0.15. He can try one of these in an hour. I was 90% certain that he would replace the battery a. What is the probability that the engine runs in an hour? b. If the engine doesn't run in an hour, what is the probability that George replaced 2.39 the starter?

Explanation / Answer

a) probability that engine runs in an hour =P( relaces the battery and engine runs+replaces the starter and engine runs)

=0.90*0.8+(1-0.9)*0.15=0.735

b) probability engine does not start =1-P( engine starts )=1-0.735-=0.265

probability that replaces the starter given engine does not start

=P(replaces the starter and engine does not runs)/P( engine does not run)=(1-0.9)*(1-0.15)/0.265=0.3208

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