Question

Your personal library contains books written by 165 authors. 60% of the authors are men. 40% of the authors write only nonfiction works. Also, 40 of the male authors write only nonfiction works. Assuming that your library has only one book by each author, what is the probability that a book picked at random is either a work written by an author who writes only nonfiction or a work written by a man?

Answer 1

The books written by men are a combination of non-fiction and fiction works. To avoid double counting we need to separate out the number of non-fiction books written by women.
There are 165 * 0.4 = 66 non-fiction books written by men or women. It is given that 40 of these works are by men. Therefore there are 66 - 40 = 26 non-fiction books written by women.
Let event A be 'select a non-fiction book written by a woman.
P(A) = 26/165 = 0.1576
Let event B be 'select a book written by a man'.
P(B) = 0.6
Events A and B are mutually exclusive, therefore the probability that a book picked at random is either a work written by an author who writes only nonfiction or a work written by a man is:

P(A) + P(B) = 0.1576 + 0.6 = you can calculate

Answer 2

whats the answer