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 e be the event that the participants first motor vehicle had eight cylinders and let t be the event that the participants first motor vehicle was a truck. what is the value of p(e or t)? motor vehicle

cylinders	car	truck	suv
six	16	12	20
eight	2	6	2

0.17
0.28
0.03
0.14

Explanation:

Step1: Find number of elements in E

The number of vehicles with eight - cylinders is \(2 + 6+2=10\).

Step2: Find number of elements in T

The number of trucks is \(6 + 12+6 = 24\).

Step3: Find number of elements in \(E\cap T\)

The number of eight - cylinder trucks is 6.

Step4: Use the formula for \(P(E\ or\ T)\)

The formula for \(P(E\ or\ T)\) is \(P(E\cup T)=P(E)+P(T)-P(E\cap T)\). Since \(P(A)=\frac{n(A)}{n(S)}\) where \(n(A)\) is the number of elements in event \(A\) and \(n(S) = 200\) (total number of participants). \(P(E)=\frac{10}{200}\), \(P(T)=\frac{24}{200}\), \(P(E\cap T)=\frac{6}{200}\). Then \(P(E\cup T)=\frac{10 + 24- 6}{200}=\frac{28}{200}=0.14\).

Answer:

0.14