Question

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.

Answer 1

Given:

`P(\text{gas)}=0.89`
`P(\text{Gas \& Oil) = 0.05}`
`P(\text{Oil) = 0.07}`

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

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

The answer is 0.71

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

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

The answer is 0.06