Question

A sample of 500 people are asked,"If you could have a new vehicle, would you want asport utility vehicle or a car?" The result of the survey counts follows:

Answer 1

The complete table would be the follwing:

A.

To get this probability, we take the total number people who pefer an SUV, and divide it by the total number of people in the sample

`P(S)=(210)/(500)`

B.

To get this probability, we take the total number of females, and divide it by the total number of people in the sample

`P(F)=(315)/(500)`

C.

To get this probability, we take the total number of females who pefer a car, and divide it by the total number of people in the sample

`P(F\cap C)=(263)/(500)`

D.

`\begin{gathered} P(F\cup S)=P(F)+P(S)-P(F\cap S) \\ \rightarrow P(F\cup S)=(315)/(500)+(210)/(500)-(52)/(500) \\ \\ \Rightarrow P(F\cup S)=(473)/(500) \end{gathered}`

E.

`\begin{gathered} P(S|M)=(P(S\cap M))/(P(S)) \\ \\ \rightarrow P(S|M)=((158)/(500))/((210)/(500)) \\ \\ \Rightarrow P(S|M)=(158)/(210) \end{gathered}`

F.

`\begin{gathered} P(M|S)=(P(M\cap S))/(P(S)) \\ \\ \rightarrow P(M|S)=((158)/(500))/((185)/(500)) \\ \\ \Rightarrow P(M|S)=(158)/(185) \end{gathered}`

In the final question we're being asked for:

`P((M\cap S)\cap(M\cap C))`

This is:

`P(M\cap S)\cdot P(M\cap C)`
`(158)/(500)\cdot(27)/(500)=0.017`

Therefore, this probability is 0.017