Answer:
P(professor or a male) = 0.7
Step-by-step explanation:
This uses the or rule for probability where events are not mutually exclusive, so we use the formula
P(A or B) = P(A) + P(B) - P(A and B)
Let A = number of professors
Let B = number of males
There are 40 total people in the pool to choose from, so
P(A) = 15/40 (there are 15 total professors)
P(B) = 19/40 (there are 6 male professors and 13 male assistants, making 19)
P(A and B) = 6/40 (there are 6 people who are both a professor and a male)
So the probability is
P(professor or male) = P(A or B) = 15/40 + 19/40 - 6/40
P(A or B) = 28/40 = 0.7
The reason we subtract P(A and B) is because we already counted male professors. If we don't subtract them, we get a wrong answer. The male professors were already counted, as well as the total amount of males, which includes the 6 that are professors. If we don't subtract that 6 out, we have counted them twice!
