t 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 0.88. If the car does not have engine trouble, the diagnostic test will turn out positive with a probability of 0.02. What is the probability of a positive engine diagnostic test? Using Bayes Theorem, calculate the probability that the car has engine trouble, if the engine diagnostic test is positive. Using Bayes Theorem, calculate the probability that the car has engine trouble if the engine diagnostic test is negative. If 20 cars arrive to the garage on a particular day, what is the probability that: (i) 7 of the cars will have engine trouble (ii) The first car with engine trouble that arrives into the garage that day will be the 9th car.
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
What is the probability of a positive engine diagnostic test?
Using Bayes Theorem, calculate the probability that the car has engine trouble, if the engine diagnostic test is positive.
Using Bayes Theorem, calculate the probability that the car has engine trouble if the engine diagnostic test is negative.
If 20 cars arrive to the garage on a particular day, what is the probability that:
-
(i) 7 of the cars will have engine trouble
-
(ii) The first car with engine trouble that arrives into the garage that day will be
the 9th car.
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