There are two known issues with a certain model of new car...

There are two known issues with a certain model of new car. The first issue, AA, occurs with a probability of P(A)=0.1P(A)=0.1. BB is another known issue with the car. If it is known that either event occurs with a probability of P(A OR B)=0.93P(A OR B)=0.93, and that both events occur with a probability of P(A AND B)=0.07P(A AND B)=0.07, calculate P(B)P(B).

Faulty Car Probabilities [11 marks] A car model unfortunately fairly commonly has faults in its engine and/or its transmission. The probability that a random new car of this model has an engine fault is 0.05. The probability that a random new car of this model has a transmission fault is 0.02. The probability that a random new car of this model has one or more of these faults is 0.06. (a) Define the events of interest (with notation), the sample space and the known probabilities. [3 marks] (b) If one of these cars has a faulty transmission, what is the probability that it also has a faulty engine? [3 marks] (c) If one of these cars has a transmission which passes all tests, what is the probability that it has a faulty engine? [3 marks] (d) If one of these cars has a faulty engine, what is the probability that it also has a faulty transmission? [2 marks]

Leslie L.

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