ESTION 3 particular garage 20% of the cars that arrive for repair have engine trouble. n arrival at the garage an engine diagnostic test is carried out on the car, but this ne diagnostic test is far from perfect. If the car has engine trouble the diagnostic will turn out positive with a probability of 0.9. If the car does not have engine ple, the diagnostic test will turn out positive with a probability of 0.05. each of the questions below explain your answer i.e. show your reasoning.

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QUESTION 3
At a particular garage 20% of the cars that arrive for repair have engine trouble.
Upon arrival at the garage an engine diagnostic test is carried out on the car, but this
engine diagnostic test is far from perfect. If the car has engine trouble the diagnostic
test will turn out positive with a probability of 0.9. If the car does not have engine
trouble, the diagnostic test will turn out positive with a probability of 0.05.
For each of the questions below explain your answer i.e. show your reasoning.
Q 3(a)
What is the probability of a positive engine diagnostic test?
Q 3(b)
Using Bayes Theorem, calculate the probability that the car has engine trouble, if the
engine diagnostic test is positive.
Q 3(c)
Using Bayes Theorem, calculate the probability that the car does not have engine
trouble, if the engine diagnostic test is negative.
Transcribed Image Text:QUESTION 3 At a particular garage 20% of the cars that arrive for repair have engine trouble. Upon arrival at the garage an engine diagnostic test is carried out on the car, but this engine diagnostic test is far from perfect. If the car has engine trouble the diagnostic test will turn out positive with a probability of 0.9. If the car does not have engine trouble, the diagnostic test will turn out positive with a probability of 0.05. For each of the questions below explain your answer i.e. show your reasoning. Q 3(a) What is the probability of a positive engine diagnostic test? Q 3(b) Using Bayes Theorem, calculate the probability that the car has engine trouble, if the engine diagnostic test is positive. Q 3(c) Using Bayes Theorem, calculate the probability that the car does not have engine trouble, if the engine diagnostic test is negative.
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