Question

customers at a certain car wash can choose between 2 plans, gold and bronze. the car wash also provides a tire shine service, which is not included in either plan. the owner collected data on 80 randomly selected customers at the car wash to learn about their preferences, which are shown in the table.

a customer will be randomly selected. what is the probability that this customer chose the gold plan, but did not choose the tire shine?

a. \\( \frac { 1 } { 3 } \\)

b. \\( \frac { 3 } { 3 } \\)

c. \\( \frac { 9 } { 20 } \\)

d. \\( \frac { 9 } { 20 } \\)

e. \\( \frac { 21 } { 40 } \\)

Explanation:

Step1: Identify the number of customers who chose Gold Plan but not tire shine

From the table, the number of customers who chose Gold Plan is \(36\). The number of customers who chose Gold Plan and tire shine is \(12\). So the number of customers who chose Gold Plan but not tire shine is \(36 - 12=24\).

Step2: Use the probability formula

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of customers is \(n = 80\). So \(P=\frac{24}{80}\).

Step3: Simplify the fraction

Simplify \(\frac{24}{80}\) by dividing both the numerator and the denominator by their greatest - common divisor. The GCD of \(24\) and \(80\) is \(8\). \(\frac{24\div8}{80\div8}=\frac{3}{10}\).

Answer:

B. \(\frac{3}{10}\)