To find the probability that a randomly selected customer purchased a rinse and wax for a van, we need to follow these steps:
1. Identify the number of customers who purchased a rinse and wax for each vehicle type.
2. Calculate the total number of customers who purchased a rinse and wax.
3. Determine the probability of a customer purchasing a rinse and wax for a van.
Let's break it down:
1. From the table, we see the number of customers who purchased a rinse and wax for each type of vehicle:
- SUV: 13 customers
- Sedan: 17 customers
- Van: 23 customers
2. Next, we calculate the total number of customers who purchased a rinse and wax:
[tex]\[
\text{Total number of rinse and wax purchases} = 13 (\text{SUV}) + 17 (\text{Sedan}) + 23 (\text{Van}) = 53
\][/tex]
3. The probability of selecting a customer who purchased a rinse and wax for a van is given by the ratio of the number of van purchases to the total number of rinse and wax purchases. Thus, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of van rinse and wax purchases}}{\text{Total number of rinse and wax purchases}} = \frac{23}{53}
\][/tex]
Since [tex]\(\frac{23}{53}\)[/tex] is already in its simplest form, the final answer is:
[tex]\[
\frac{23}{53}
\][/tex]
Therefore, the probability that a randomly chosen customer purchased a rinse and wax for a van is approximately [tex]\(0.4339622641509434\)[/tex].
