Question

The physics department of a college has 8 male professors, 11 female professors, 16 male teaching assistants, and 6 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.

Answer 1

To determine the probability that one or the other circumstances will occur, you will count the number of possible outcomes and divide it by all the possible outcomes.

#of female teaching assistants + # of male teaching assistants + # of female professors

6 + 16 + 11 = 33

Total = 41

33/41 = 80

There is a approximate 80% probability that one or the other will occur.

Answer 2

$|\Omega|=41\\ |A|=\underbrace{22}_{\text{teaching assistants}}+\underbrace{17}_{\text{female}}-\underbrace{6}_{\text{female teaching assistants}}=33\\\\ P(A)=\dfrac{33}{41}\approx80\%$