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Of the drivers who stop at a gas station, 89% purchase gasoline, and 5% purchase both gasoline and oil. A total of 7% purchase oil.(a)What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to the nearest hundredth. (b)What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to the nearest hundredth.

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SOLUTION

Given:

[tex]P(\text{gas)}=0.89[/tex][tex]P(\text{Gas \& Oil) = 0.05}[/tex][tex]P(\text{Oil) = 0.07}[/tex]

(a)What is the probability that a driver purchases gasoline, given that he or she purchases oil:

[tex]=\frac{P(\text{Gas \& Oil)}}{P(Oil)}[/tex][tex]=\frac{0.05}{0.07}[/tex][tex]\begin{gathered} =0.71429 \\ =0.71\text{ (to the nearest hundredth)} \end{gathered}[/tex]

The answer is 0.71

b) What is the probability that a driver purchases oil, given that he or she purchases gasoline:

[tex]\begin{gathered} =\frac{P(\text{Gas \& Oil)}}{P(Gas)} \\ =\frac{0.05}{0.89} \\ =0.05617 \\ =0.06\text{ (to the nearest hundredth)} \end{gathered}[/tex]

The answer is 0.06

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