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Of the drivers who stop at a gas station, 91% purchase gasoline, and 5% purchase both gasoline and oil. A total of 9% purchase oil. (a) What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to 2 decimal places. (b) What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to 2 decimal places.

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JeanaShupp

Answer: a) 0.05

b) 0.56

Step-by-step explanation:

Let A be denote the event that gas station purchase gasoline.

B be denote the event that gas station purchase oil.

As per given description, we have

P(A)-0.91   , P(B)= 0.09  ,    P(A ∩B)=0.05

Then, the probability that a driver purchases oil, given that he or she purchases gasoline will be :-

[tex]P(B|A)=\dfrac{P(A\cap B )}{P(A)}[/tex]  [Conditional probability formula.]

[tex]P(B|A)=\dfrac{0.05}{0.91}=\dfrac{5}{91}\\\\=0.0549450549451\approx0.05[/tex]

Similarly , The probability that a driver purchases gasoline, given that he or she purchases oil will be :-

[tex]P(A|B)=\dfrac{P(A\cap B )}{P(B)}[/tex]

[tex]P(A|B)=\dfrac{0.05}{0.09}=\dfrac{5}{9}\\\\=0.555555555556\approx0.56[/tex]

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