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)