Of the drivers who stop at a gas station, 89% purchase gasoline, and 6% purchase both gasoline and oil. A total of 9% purchase oil.

(a) What is the probability that a driver purchases gasoline, given that he or she purchases oil? Round your answer to 2 decimal places.

(b) What is the probability that a driver purchases oil, given that he or she purchases gasoline? Round your answer to 2 decimal places.

I got a)14.83
and b) 15

can you please help

Think about it. How can you have a probability of 14.83 and 15? Probabilities go from 0 to 1, inclusive. 0 for no probability to 1 for 100% probability.

Build a chart. That helps. Assume 1000 total customers:



\begin{tabular}{ l | c |c| r | }
\hline
& OIL & NO OIL&TOTAL \\ \hline
GAS & 60 &830&890 \\ \hline
NO GAS & 30 & 80&110 \\ \hline
TOTAL&90&910&1000\\ \hline

\end{tabular}



Now, for part a, prob. They purchase gas given they purchase oil.

Go across the gas row to the oil column, then go down.

We get 60/90=2/3.

Or, \frac{.06}{.09}=0.\overline{6}


Part b, prob. Buy oil given they buy gas.

Go to the OIL and column, then go across the GAS row.

We get 60/890=6/89

P(O|G)=\frac{P(\text{O and G})}{P(\text{O and G})+P(\text{No Oil and Gas})}=\frac{.06}{.06+.83}


See how to do them now? If coming up with the probability equation is confusing, build a chart. Then, you can answer whatever they throw at you.

What is the prob. They do not buy gas given they buy oil?

Go across the NO GAS row and down the OIL column. 30/90=1/3.