What is the probability of eating pizza for dinner given that they buy a new car?

Question

The probability of eating pizza for dinner is 34% and the probability of buying a new car is 15%. The probability of buying a new car given that you eat pizza for dinner is 42%. What is the probability of eating pizza for dinner given that they buy a new car?

Answer 1

If there are two events, A and B, with P(A) and P(B), and P(A,B) (Probability of A and B), then the conditional probability of A given B is

P(A|B) = P(A,B) / P(B)

In this question:

P(Eat Pizza) = 0.34

P(Buy Car) = 0.15

P(Buy Car | Eat Pizza) = 0.42

We need to find:

P(Eat Pizza | Buy Car) = P(Eat Pizza, Buy Car) / P(Buy Car)

You can find P(Eat Pizza, Buy Car), using the given information P(Buy Car) and P(Buy Car | Eat Pizza). Then you have everything you need to calculate P(Eat Pizza | Buy Car).