Question

of the drivers who stop at a gas station, 93% purchase gasoline, and 6% purchase both gasoline and oil. a total of 8% purchase oil. answer the questions below. (if necessary, consult a list of formulas.) (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.

Explanation:

Step1: Define events and probabilities

Let $A$ be the event that a driver purchases gasoline and $B$ be the event that a driver purchases oil. We know $P(A)=0.93$, $P(A\cap B) = 0.06$ and $P(B)=0.08$.

Step2: Use the formula for conditional - probability

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$ and $P(A|B)=\frac{P(A\cap B)}{P(B)}$.

(a) Calculate $P(B|A)$

$P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{0.06}{0.93}\approx0.06$.

(b) Calculate $P(A|B)$

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.06}{0.08} = 0.75$.

Answer:

(a) $0.06$
(b) $0.75$