John is going to buy a new car. He will purchase a car with one of the following

Question

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?

Explanation / Answer

a)

Body types: 2

Manufacturers: 4

Colors: 5

Total choices: 2 X 4 X 5 = 40

b) He can choose 4 black sedan from 40 options, so the probability is 4/40=0.1=10%

c) There are 3 colors, 4 manufacturers and 2 body types. He can choose 3x4x2=24 cars from 40, so the probability is 24/40=0.6=60%

d) F'=it isn't a ford, S=choose a silver car

P(F'S)=6/40=0.15

P(S)=8/40=0.2

P(F'/S)=0.15/0.2=0.75

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