Question

Fill ’er up Refer to Exercise 83. Given that the customer paid with a credit card, find the probability that she bought premium gas.

Short answer

The probability that she bought premium gas is $14.23\%$

Step-by-step solution

Step 1. Given Information

Regular gasoline was purchased by $88\%$ of the vehicles, while midgrade gas was purchased by $2\%$ and premium gas was purchased by 10%. On regular gas, $28\%$ is paid with a credit card, $34\%$ is paid on midgrade gas, and $42\%$ is paid on premium gas.

Step 2. Concept Used

Condition probability: $P(A/B)=P(A\cap B)/P\left(B\right)$

Step 3. Calculation

The tree diagram is shown below, according to the question:

$$\begin{gathered} P(creditcard)=0.2952 \\ P(Premium\cap creditcard)=0.0420 \end{gathered}$$

Condition probability: $P(A/B)=P(A\cap B)/P\left(B\right)$

As a result, the following was obtained:

$P(Premium/creditcard)=\frac{P(Premium\cap creditcard)}{P(Creditcard)}$

$=\frac{0.420}{0.2952}=0.1423=14.23\%$

As a result, there's a $14.23\%$chance she bought premium gas.