The following table shows the results of a coffee taste test given at a local grocery store. \begin{tabular}{|c|c|c|c|} \hline Coffee & Brand A & Brand B & Total \\ \hline Men & 512 & 938 & 1450 \\ Women & 338 & 660 & 998 \\ \hline Total & 850 & 1598 & 2448 \\ \hline \end{tabular} a) If one of these individuals is selected at random, find the probability that they prefer Brand A coffee. b) If one of these individuals is selected at random, find the probability that they prefer Brand A coffee, given that a man is selected. a) The probability that they prefer brand A coffee is (Round to four decimal places as needed.) b) The probability that they prefer Brand A coffee, given that a man is selected, is (Round to four decimal places as needed.)

Step 1 ：Given the total number of individuals is 2448, the total number of individuals who prefer Brand A is 850, the total number of men is 1450, and the number of men who prefer Brand A is 512.

Step 2 ：To find the probability that a randomly selected individual prefers Brand A coffee, we divide the total number of individuals who prefer Brand A by the total number of individuals. This gives us \(\frac{850}{2448} = 0.3472\).

Step 3 ：To find the probability that a randomly selected individual prefers Brand A coffee, given that the individual is a man, we divide the number of men who prefer Brand A by the total number of men. This gives us \(\frac{512}{1450} = 0.3531\).

Step 4 ：Final Answer: a) The probability that they prefer brand A coffee is \(\boxed{0.3472}\). b) The probability that they prefer Brand A coffee, given that a man is selected, is \(\boxed{0.3531}\).