If a person is selected at random from the group, find the probability that the person is a professor or is a male.

Question

the mathematics department of a college has 8 male professors, 12 female professors,14 male teaching assistants, and 10 female teaching assistants. If a person is selected at random from the group, find the probability that the person is a professor or is a male.

Answer 1

There are 8 + 12 + 14 + 10 = 44 people in the group.  

 

The only way to NOT select a professor or a male is to select a female teaching assistant, of which there are 10.  So any of the other 34 selections will be a professor or be male, so P(professor or male) = 34/44 = 17/22.  

 

You could also determine the 34 selections that satisfy the conditions by adding up 8 male professors + 12 female professors + 14 male teaching assistants = 34 people who are a professor or male.