Probability !

the mathematics department of a college has 6 male professors, 9 female professors, 13 male teaching assistants, and 12 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.

the probability is:

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!

only 10/60 isn't equivalent

hope this : )