6. [10 points] At a certain gas station, 50%ofthe plus gas, and 20% purchase pre

Question

6. [10 points] At a certain gas station, 50%ofthe plus gas, and 20% purchase premmm gas. Ofthose rs their tanks. Of those customers purchasing premium gas, 60% fill their tanks. Suppose that a custo or if the pas anon ir selected at random purchasing plus gas, 50% fill ther taka, whereas ofthose (a) Find the probability that they purchase regular gas and fill their tank (3 points (b) Find the probability tha they fill their tank (3 points) (e) If they fill their tank, what is the probability that they had purchased plus gax? 14 pointa

Explanation / Answer

a) P( purchase regular gas and fill their tanks) =0.5*0.4 =0.20

b) P( fill the tank) =P( purchase regular gas and fill their tanks+purchase plus gas and fill their tanks+purchase premium gas and fill their tanks) =0.5*0.4+0.3*0.5+0.2*0.6=0.47

c)P(purchased plus gas given fill the tanks) =P(purchase plus gas and fill their tanks)/P(fill the tanks)

=0.3*0.5/0.47=0.3191

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