The mathematics department of a college has 5 male professors, 11 female professors, 9 male teaching assistants, and 5 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.

We need the total count of persons = 5 + 11 + 9 + 5 = 30 persons

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

= 11 female professors + (9+5) teaching assistants

= 11 + 14

= 25 persons

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

probability of choosing a female or teaching assistant

= 25/30

= 5/6

(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, 5/6=0.83333 ... = 0.833 approximately)