Suppose the people in a room are divided into two groups as follows:

Members: 15 men, 20 women, 0 children Nonmembers: 10 men, 8 women, 12 children

A prize is given to one person who is selected at random by first choosing one group or the other, with members \(M\) being twice as likely to be chosen as nonmembers \(\bar{M}\). After the group is selected, then one person in that group is selected, with each person in the group having an equal chance of being chosen. Let \(N=\{\) a man is chosen \(\}, W=\) \{a woman is chosen \(\}\), and \(C=\{\) a child is chosen \(\}\). Use this information for Problems 47-52.

\(P(\bar{M} \mid N)\)