\begin{tabular}{|cr|r|r|} \hline \multicolumn{8}{c}{ Smoking by Race for Males Aged 18 to 24} \\ \hline White (W) & Smoker (S) & Nonsmoker $(N)$ & Row Total \\ Black (B) & 255 & 571 & 826 \\ Column Total & 12 & 162 & 174 \\ \cline { 2 - 5 } & 267 & 733 & 1,000 \\ \hline \end{tabular} Click here for the Excel Data File: (a) Calculate the probabilities given below: (Round your answers to 4 decimal places.) \begin{tabular}{|c|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 total number of people surveyed is 1000, total number of smokers is 267, total number of non-smokers is 733, total number of white people is 174, total number of black people is 826, number of white smokers is 12, number of black smokers is 255, and number of black non-smokers is 571.

Step 2 ：Calculate the probability of a person being a smoker, denoted as \(P(S)\), which is the total number of smokers divided by the total number of people surveyed. So, \(P(S) = \frac{267}{1000} = 0.2670\).

Step 3 ：The probability of \(P(M)\) is not defined in the problem as we don't have any information about 'M'.

Step 4 ：Calculate the probability of a person being a smoker given they are white, denoted as \(P(S | W)\), which is the number of white smokers divided by the total number of white people. So, \(P(S | W) = \frac{12}{174} = 0.0690\).

Step 5 ：Calculate the probability of a person being a smoker given they are black, denoted as \(P(S | B)\), which is the number of black smokers divided by the total number of black people. So, \(P(S | B) = \frac{255}{826} = 0.3087\).

Step 6 ：Calculate the probability of a person being a smoker and white, denoted as \(P(S \text{ and } W)\), which is the number of white smokers divided by the total number of people surveyed. So, \(P(S \text{ and } W) = \frac{12}{1000} = 0.0120\).

Step 7 ：Calculate the probability of a person being a non-smoker and black, denoted as \(P(N \text{ and } B)\), which is the number of black non-smokers divided by the total number of people surveyed. So, \(P(N \text{ and } B) = \frac{571}{1000} = 0.5710\).

Step 8 ：So, the probabilities are: \(\boxed{P(S) = 0.2670}\), \(P(M)\) is not defined, \(\boxed{P(S | W) = 0.0690}\), \(\boxed{P(S | B) = 0.3087}\), \(\boxed{P(S \text{ and } W) = 0.0120}\), and \(\boxed{P(N \text{ and } B) = 0.5710}\).