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: Find the number of participants in \(F^C\) and \(U\)

\(F^C\) means the event that the vehicle does not have four - cylinders (i.e., has six or eight cylinders). For SUVs, the number of six - cylinder SUVs is \(20\) and the number of eight - cylinder SUVs is \(2\). So the number of participants in \(F^C\) and \(U\) is \(20 + 2=22\).

Step2: Calculate the probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of outcomes \(n = 200\). So \(P(F^C\text{ and }U)=\frac{22}{200}\)

$$ \frac{22}{200}=0.11 $$

Answer:

\(0.11\) (the third option)