A certain make of car comes with either an automatic or manual transmission and in one of

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A certain make of car comes with either an automatic or manual transmission and in one of three styles: convertible, sedan, or SUV. The following table shows the probability of each possible style and transmission.

Convertible Sedan SUV Automatic 0.32 0.27 0.21 Manual 0.08 0.05 0.07

(a) Find the probability that a car is an automatic.

(b) Find the probability that a car is an automatic given that it is an SUV.

(c) Are “automatic” and “SUV” independent? Explain.

(d) Find the probability that a car is a convertible given that it is a manual.

(e) Are “convertible” and “manual” independent? Explain.

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