Problem Solving

A focus group is currently made up of \(x\) men and y women. If \(2\) men and \(4\) women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?

A. \(\dfrac{x}{x + 2}\)
B. \(\dfrac{x}{x + y}\)
C. \(\dfrac{x + 2}{x + y + 2}\)
D. \(\dfrac{y + 4}{x + y + 6}\)
E. \(\dfrac{x + 2}{x + y + 6}\)

Answer: E

Source: Princeton Review

Total men in the group: x+2
Total women in the whole group: y+4
Total men and women: x+y+6

Thus probability to select men is: (Number of men) / (Total number of men and women)

\(\frac{x+2}{x+y+6}\)