4. At a certain gas station, 40% of the customers use regular gas, 35% use plus

Question

4. At a certain gas station, 40% of the customers use regular gas, 35% use plus gas and 25% use premium. Of those customers using regulargas only30% fill up their tank. Of those customers using plus, 60% fill up their tanks, whereas of those using premium 50% fill their tanks. What is the probability that the next customer fills up their tank and uses plus gas? a. ANS: b. What is the probability that the next customer fills up their tank? ANS c. Given that the next customer fills up their tank, what is the probability that they used Plus gas? ANS:

Explanation / Answer

A) P(next customer fills tank and uses plus gas) = 0.35x0.6 = 0.21

B) P(next customer fill up tank) = P(regular and fill tank)+ P(plus and fill tank) + P(preminum and fill tank)

= 0.4x0.3 + 0.35x0.6 + 0.25x0.5

= 0.12 + 0.21 + 0.125

= 0.455

C) P(plus gas | fills tank) = P(plus and fills tank)/ P(fills tank)

= 0.21/0.455

= 0.4615

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