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

$P(S)=\frac{210}{500}$

B.

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

$P(F)=\frac{315}{500}$

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

$P(F\cap C)=\frac{263}{500}$

D.

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

E.

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

F.

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

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)$$\frac{158}{500}\cdot\frac{27}{500}=0.017$

Therefore, this probability is 0.017