Refer to the contingency table shown below.
\begin{tabular}{|c|c|c|c|}
\hline 60 & dace for $\mathrm{Mal}$ & Aged 18 to 24 & \\
\hline & Smoker (S) & Nonsmoker $(N)$ & Row rotal \\
\hline White (W) & 259 & 553 & 812 \\
\hline Black (B) & 38 & 150 & 188 \\
\hline Column Total & 297 & 703 & 1,060 \\
\hline
\end{tabular}

Click here for the Excel Data File
(a) Calculate the probabilities given below: (Round your answers to 4 decimal
\begin{tabular}{|l|l|l|}
\hline i & $P(S)$ \\
\hline ii & $P(M)$ \\
\hline iii & $P(S \mid W)$ \\
\hline iv & $P(S \mid B)$ \\
\hline$v$ & $P(S$ and $W)$ \\
\hline vi & $P(N$ and $B)$ \\
\hline
\end{tabular}

Step 1 ：Given the contingency table, we are asked to calculate several probabilities.

Step 2 ：The total number of people in the study is 1060.

Step 3 ：The number of smokers is 297, the number of males is 60, the number of white smokers is 259, the number of black smokers is 38, the total number of white people is 812, the total number of black people is 188, and the number of non-smoker black people is 150.

Step 4 ：We use the formula for probability which is the number of favorable outcomes divided by the total number of outcomes.

Step 5 ：To calculate the probability of being a smoker, we divide the number of smokers by the total number of people: \(P(S) = \frac{297}{1060} = \boxed{0.2802}\).

Step 6 ：To calculate the probability of being a male, we divide the number of males by the total number of people: \(P(M) = \frac{60}{1060} = \boxed{0.0566}\).

Step 7 ：To calculate the probability of being a smoker given that the person is white, we divide the number of white smokers by the total number of white people: \(P(S|W) = \frac{259}{812} = \boxed{0.3190}\).

Step 8 ：To calculate the probability of being a smoker given that the person is black, we divide the number of black smokers by the total number of black people: \(P(S|B) = \frac{38}{188} = \boxed{0.2021}\).

Step 9 ：To calculate the probability of being a smoker and white, we divide the number of white smokers by the total number of people: \(P(S \text{ and } W) = \frac{259}{1060} = \boxed{0.2443}\).

Step 10 ：To calculate the probability of being a non-smoker and black, we divide the number of non-smoker black people by the total number of people: \(P(N \text{ and } B) = \frac{150}{1060} = \boxed{0.1415}\).