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 40% fill their tanks (event B). Of those customers using plus, 80% fill their tanks, whereas of those using premium, 70% fill their tanks.

Required:

a. What is the probability that the next customer will request extra unleaded gas and fill the tank?

b. What is the probability that the next customer fills the tank?

c. If the next customer fills the tank, what is the probability that regular gas is requested?

A) 0.28

B) 0.615

C) 0.26

Step-by-step explanation:

We are given;

Probabilities of customers using regular gas:P (A1) = 40% = 0.4

Probabilities of customers using plus gas: P (A2) = 35% = 0.35

Probabilities of customers using premium gas: P (A3) = 25% = 0.25

We are also given with conditional probabilities of full gas tank:

P (B|A1) = 40% = 0.4

P (B|A2) = 80% = 0.8

P (B|A3) = 70% = 0.7

A) The probability that next customer will requires extra unlead gas (plus gas) and fill the tank is:

P (A2 ∩ B) = P (A2) * P (B|A2)

P (A2 ∩ B) = 0.35 * 0.8

P (A2 ∩ B) = 0.28

B) The probability of next customer filling the tank is:

P (B) = [P (A1) • P (B|A1) ] + [P (A2) • P (B|A2) ] + [P (A3) • P (B|A3) ]

P (B) = (0.4 * 0.4) + (0.35 * 0.8) + (0.25 * 0.7)

P (B) = 0.615

C) If the next customer fills the tank, probability of requesting regular gas is;

P (A1|B) = [P (A1) • P (B|A1) ]/P (B)

P (A1|B) = (0.4 * 0.4) / 0.615

P (A1|B) = 0.26