88% of automobile drivers filled their vehicles with regular
gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Of
those who bought regular gas, 28% paid with a credit card; of
customers who bought midgrade and premium gas, 34% and 42%,
respectively, paid with a credit card. Suppose we select a
customer at random.
a) What’s the probability that the customer paid with a credit card?
b) Of the customers that paid with a credit card, what proportion bought premium gas?
Scroll down for the solution.
P(CC) = P(CC and R) + P(CC and MG) + P(CC and P) =
= 88% of 0.28 + 2% of 0.34 + 10% of 0.42 = 0.2464 + 0.0068 + 0.042 = 0.295
b) P(P | CC) = P(P and CC)/P(CC) = 0.042/0.295 = 0.1423