John is going to buy a new car He will purchase a car with o

John is going to buy a new car. He will purchase a car with one of the following body types: sedan or hatchback. He will also choose from among manufacturers: Honda, Ford, Kia, or Chevrolet. He will choose from among 5 colors: black, white, red, silver, or blue. Assume that all choices are equally likely. a) How many different choices of vehicles does John have? b) What is the probability that John chooses a black sedan? c) What is the probability that John chooses a red, white, or blue car? d) Given that John chooses a silver car, what is the probability that it is not a Ford?

Solution

a)

There are

(2 body)*(4 brands)*(5 colors) = 40 choices [ANSWER]

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b)

P(black sedan) = P(black) P(sedan) = (1/5)(1/2) = 1/10 = 0.1 [ANSWER]

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c)

There are 5 colors, so

P(red, white, or blue) = 3/5 = 0.6 [ANSWER]

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d)

Colors are brands are independent, so it doesn\'t matter if it is silver.

Hence, as there are 4 brands,

P(not Ford) = 1 - 1/4 = 3/4 or 0.75 [ANSWER]