A certain kind of passenger car comes equipped with either an automatic (A) or a

Question

A certain kind of passenger car comes equipped with either an automatic (A) or a manual (M) transmission, and the car is available in one of three different models. The following table gives proportions of car sales for the various categories. What is the probability that the next car sold of this kind is a VE model or has a manual transmission? Suppose a car of this kind has just been sold and it is not an LE model. Given this information, what is the probability that this car has an automatic transmission? What is the probability that the next two cars sold (independently) of this kind are both of the same model?

Explanation / Answer

Excel formula:

Model VE CD LE marginal probability for each transmission type Transmission type A 0.32 0.18 0.25 0.75 M 0.16 0.06 0.03 0.25 marginal probability for each model 0.48 0.24 0.28 1 4 P(VE or Manual)= P(VE)+P(Manual)- P(VE, Manual) 0.57 5 P(A|LE')=[P(A|VE)+P(A|CD)]/[P(VE) + P(CD)] P(A,LE')= 0.5 P(LE')= 0.72 P(A|LE')= 0.694444 6 2 cars of same model= P(both VE model) or P(both CD model) OR P(both LE model) 0.3664

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