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Chapter 5: Q 85. (page 331)

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

Expert verified

The probability that she bought premium gas is 14.23%

Step by step solution

01

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.

02

Step 2. Concept Used

Condition probability: P(A/B)=P(A∩B)/P(B)

03

Step 3. Calculation

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

P(creditcard)=0.2952P(Premium∩creditcard)=0.0420

Condition probability: P(A/B)=P(A∩B)/P(B)

As a result, the following was obtained:

P(Premium/creditcard)=P(Premium∩creditcard)P(Creditcard)

=0.4200.2952=0.1423=14.23%

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

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