In Exercise 59, consider the following additional information on credit card usage:

70% of all regular fill-up customers use a credit card.

50% of all regular non-fill-up customers use a credit card.

60% of all plus fill-up customers use a credit card.

50% of all plus non-fill-up customers use a credit card.

50% of all premium fill-up customers use a credit card.

40% of all premium non-fill-up customers use a credit card.

In Exercise 59

At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.

Compute the probability of each of the following events for the next customer to arrive (a tree diagram might help).

a. {plus and fill-up and credit card}

b. {premium and non-fill-up and credit card}

c. {premium and credit card}

d. {fill-up and credit card}

e. {credit card}

f. If the next customer uses a credit card, what is the probability that premium was requested?