To solve this problem, we need to determine the probability that a randomly selected customer purchased a job for a sedan or a wax.
Let's follow these steps:
1. Calculate the total number of customers for each service type and for each vehicle type:
- Rinse Service:
- SUV Rinse: 11
- Sedan Rinse: 31
- Van Rinse: 41
- Total Rinse = 11 + 31 + 41 = 83
- Wax Service:
- SUV Wax: 7
- Sedan Wax: 19
- Van Wax: 29
- Total Wax = 7 + 19 + 29 = 55
- Rinse and Wax Service:
- SUV Rinse and Wax: 13
- Sedan Rinse and Wax: 17
- Van Rinse and Wax: 23
- Total Rinse and Wax = 13 + 17 + 23 = 53
2. Calculate the total number of customers at the carwash for the week:
- Total Customers = Total Rinse + Total Wax + Total Rinse and Wax
- Total Customers = 83 + 55 + 53 = 191
3. Calculate the number of customers who purchased a service for a sedan or a wax:
- Customers who purchased service for a sedan:
- Sedan Rinse: 31
- Sedan Wax: 19
- Sedan Rinse and Wax: 17
- Total Sedan Customers = 31 + 19 + 17 = 67
- Total Wax Customers (already calculated):
- Total Wax = 55
- To avoid counting those who purchased a wax for a sedan service twice, we need to count each only once. Hence, sum the results for total sedan customers and total wax customers.
- Sedan or Wax Customers = Total Sedan Customers + Total Wax (since there is a double overlap, they do not add but rather one occurs within both):
- Sedan or Wax Customers = 67 + 55 = 122
4. Calculate the probability that a randomly selected customer purchased a job for a sedan or a wax:
- Probability = (Number of Customers who purchased a Sedan or Wax) / (Total Number of Customers)
- Probability = 122 / 191
So, the probability that a randomly selected customer purchased a job for a sedan or a wax is [tex]\( \frac{122}{191} \)[/tex] or approximately [tex]\( 0.6387 \)[/tex].
