Question

insurance company executives surveyed 200 young adults about their first motor vehicle. the results are shown in the two - way table. a survey participant is randomly selected. let f be the event that the participants first motor vehicle had four cylinders and let u be the event that the participants first motor vehicle was an suv. what is the value of p(f^c and u)?

Explanation:

Step1: Define the complement of event F

$F$ is the event that the first - motor vehicle had four cylinders. So, $F^{C}$ is the event that the first - motor vehicle had six or eight cylinders.

Step2: Find the number of elements in $F^{C}$ and $U$

The number of vehicles that are SUVs and have six cylinders is 20, and the number of vehicles that are SUVs and have eight cylinders is 2.
The number of elements in the intersection of $F^{C}$ and $U$ is $20 + 2=22$.

Step3: Calculate the probability

The total number of surveyed young adults is $n = 200$.
The probability $P(F^{C}\text{ and }U)=\frac{\text{Number of elements in }(F^{C}\cap U)}{\text{Total number of elements}}=\frac{22}{200}=0.11$

Answer:

0.11