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.

choose tire shine	choose gold plan	choose bronze plan	total
total	36	44	80

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. $\frac{1}{4}$
c. $\frac{3}{10}$
d. $\frac{9}{20}$
e. $\frac{9}{25}$

Explanation:

Step1: Identify the number of favorable outcomes

The number of customers who chose the Gold Plan but did not choose the tire shine is \(12\).

Step2: Identify the total number of outcomes

The total number of customers is \(80\).

Step3: Calculate the probability

The probability \(P\) is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{12}{80}\). Simplify \(\frac{12}{80}=\frac{3}{20}\).

Answer:

\(\frac{3}{20}\) (Option E)