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

Question

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

a.       What is the probabilitythat the next customer will request extra unleaded gas and fill thetank?

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

c.       If the next customerfills the tank, what is the probability that regular gas isrequested? Extra gas? Premium gas?

Explanation / Answer

P(BA2) = P(B|A2)*P(A2) = 0.6 * 0.35 = 0.21
b. This probability that the tank is filled is given by:
P(B) = P(B|A1)P(A1) + P(B|A2)P(A2) + P(B|A3)P(A3) = (0.3)(0.4)+ (0.6)(0.35) + (0.5)(0.25) = 0.455
c. The probability that EXTRA gas isrequested given the tank is filled is:
P(A2|B) = P(BA2) / P(B) = (part a / part b from above)= 0.21 / 0.455 = 0.462
To calculate regular and premium gas for part c, first solvefor the probability that the next customer will request that typeof gas and fill the tank by using the method in part a, and thendivide by part b.
Hope this helps

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