A plumbing company needs to hire 2 plumbers. Four people (3 men and 1 woman) apply for the job. Since they are all equally qualified, the selection is made at random (2 names are pulled out of a hat). What is the probability that only one man is hired?

Question

whpalmer4 · Answer

To hire only one man, obviously one of the two names chosen must be that of the woman.
For the first drawing, the probability of drawing the woman is 1 in 4.  With such a small number of outcomes, an outcome tree should be easy to draw.  The first level will represent the first person chosen, and the second level will be all the possible outcomes.  Count up the number of outcomes that include choosing a woman, and divide by the number of total outcomes.  What do you get?