The mathematics department of a college has 10 male professors, 12 female professors, 12 male teaching assistants, and 15 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.

We need the total count of persons = 10+12+12+15 = 49 persons

We need the count of the target group, female or teaching assistants

= (10+12) professors + 12 male teaching assistants

= 22+12

= 34 persons

Assuming equal probability of choosing anyone from the 30 persons, the

probability of choosing a professor or a male

= 34/49

(For probability calculations, try to keep a fraction for as long as you can, because fractions are exact. Decimal are frequently approximate, for example in this case, 34/49=0.693877551020 ... = 0.694 approximately)