Of the drivers who stop at a gas station, 92% purchase gasoline, and 6% purchase both gasoline and oil. A total of 7% purchase oil.

Questions:

(a) What is the probabilitythat a driver purchases gasoline, given that he or she purchases oil?

(b) What is the probability that a driver purchases oil, given that he or she purchases gasoline?

This kind of problem is easier if we assume that there are a total of 100 people (even if the number of people is different, all the percentages will remain the same and your answers will be correct). You can choose any number of people you want, but 100 is the easiest to work with.

So, if there are 100 people in total, then 92 of them purchase gas and 7 of them purchase …

This solution is comprised of a 270 word response which provides an explanation of the scenario at hand in simplified terms first, before approaching these two questions based on conditional probability. All calculations and work are included with the response.