Question

Assume that the car lot contains 35 percent Volvos, 25 percent Porches, and 40 percent BMWs. Of the Volvos, 70 percent have two airbags, 80 percent of the Porches have two airbags, and 20 percent of the BMWs have two airbags. You are assigned a car at random. If the car has two airbags, what is the probability that it is not a Volvo?

Answer 1

We can think about this in two way. As a math-y conditional probability problem (which it is), or as a parking lot (which it also is).

Iff there are 1000 cars:
Volvos: 350
Porches: 250
BMW: 400

Volvos with airbags: (350)(0.7) = 245
Porches with airbags: (250)(0.8) = 200
BMW's with airbags: (400)(0.2) = 80

This is equivalent to drawing out a tree diagram of the probabilities where the cars are the first branches and the air-bagginess are the secondary branches.