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

@jaydons Welcome to Question Cove. How far have you gotten with solving this one?

Answer 2

Welcome to QuestionCove!

This is the information that the question gives you:
165 books, 165 authors

60% of the authors are men
40% of the authors write only nonfiction
40 of the male authors write only nonfiction works


We want to find the probability of picking a book that is either written by an author who writes only nonfiction OR a work written by a man.

We need to use this formula
P(A or B) = P(A) + P(B) - P(A and B)

Applying that to your case:
P(only nonfiction or man) = P(only write nonfiction) + P(male author) - P(male author who writes only nonfiction)

You are already given the probability of authors who only write nonfiction, and the probability of male authors.
You need to find the probability of a male author writing only nonfiction. They told you that there are 40 male authors who only write nonfiction. There is a total of 165 authors. Find the probablity of that.

Now you have all three numbers and you can plug it into the formula above.

(Remember: the probability is a number between 0 and 1. That means a 50% chance is a probability of 0.5)