At a certain gas station, 40% of the customers use regulargas (A1), 35 % use plus gas (A2) and 25 % usepremium (A3). Of those customers using regular gas, only30 % fill their tanks (event B). Of those customers using plus, 60 %fill their their tanks, whereas of those premium, 50 % fill theretanks.

a) What is the probability that the next customer will requestplus gas and fill their tank?

b) What is the probability that the next customer fills thetank?

c) If the next customer fills the tank, what is the probabilitythat the regular gas is requested? Plus? Premium

a) P (A2 & B) = 0.21

b) P (B) = 0.455

c) P (A1/B) = 0.2637, P (A2/B) = 0.4615, P (A3/B) = 0.2747

Step-by-step explanation:

Given:

- P (A1) = 0.40

- P (A2) = 0.35

- P (A3) = 0.25

- P (B / A1) = 0.3

- P (B / A2) = 0.6

- P (B / A3) = 0.5

Find:

a) What is the probability that the next customer will request plus gas and fill their 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 the regular gas is requested? Plus? Premium

Solution:

a)

- The probability that the next customer fill plus gas for complete tank is:

P (A2 & B) = P (A2) * P (B/A2)

P (A2 & B) = 0.35*0.6

P (A2 & B) = 0.21

b)

- The probability that the next customer fill complete tank is:

P (B) = P (A2) * P (B/A2) + P (A1) * P (B/A1) + P (A3) * P (B/A3)

P (B) = 0.21 + 0.4*0.3 + 0.25*0.5

P (B) = 0.455

c)

- The probability that the next customer fill complete tank what is the probability that each of the gas is requested

P (A1/B) = P (A1 & B) / P (B)

P (A1/B) = 0.4*0.3/0.455

P (A1/B) = 0.2637

P (A2/B) = P (A2 & B) / P (B)

P (A2/B) = 0.21/0.455

P (A2/B) = 0.4615

P (A3/B) = P (A3 & B) / P (B)

P (A3/B) = 0.25*0.5/0.455

P (A3/B) = 0.2747