At a certain gas station, 40% of customers use regular unleaded gas (A 1 ), 35%

Question

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

a) Display this information in a probability tree diagram.

b) What is the probability that the next customer will request special unleaded gas and fill the tank (A2 and B)?

c) What is the probability that the next customer fills the tank?

d) If the next customer fills the tank, what is the probability that regular gas was requested? Special? Premium? Provide all three probabilities.

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 special fill-up customers use a credit card.

50% of all special 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.

e) Build another tree diagram adding the above information.

f) What is the probability that the next customer uses special gas and fills-up and uses a credit card?

g) What is the probability that the next customer uses premium and does not fill up and uses a credit card?

h) What is the probability that the next customer uses premium and a credit card?

i) What is the probability that the next customer uses a credit card?

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

PLEASE ANSWER FROM E TO J

Explanation / Answer

A1=0.4 A2 =0.35 A3=0.25

B =0.12 Not B=0.28 B=0.21 Not B=0.14 B=0.125 Not B=0.125

b)P( A2 and B) = 0.21

c) P(B)= 0.12+0.21+0.125=0.455

d) P( Regular/Filled) = 0.12/[0.455]

P(Special/Filled)=0.21/0.455

P(Premium/Filled]=0.124/0.455

Please repost the other questions individually

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