Question

The mathematics department of a college has 9 male​ professors, 11 female​ professors, 10 male teaching​ assistants, and 11 female teaching assistants. If a person is selected at random from the​ group, find the probability that the selected person is a professor or a male.

Answer 1

There are 9 male professors, and 11 female professors. So there are 9+11 = 20 professors total.

There are 9 male professors and 10 male teaching assistants. So there are 9+10 = 19 males total

Add up the two subtotals: 20+19 = 39

The overlap of the two groups (9 male professors) needs to be subtracted off since we counted this group twice: 39-9 = 30

So there are 30 people who are a professor, male, or both

This is out of 9+11+10+11 = 41 people total

The answer as a fraction is exactly 30/41
The approximate answer in decimal form is 0.7317