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

Answer:

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 75.8%.

Step-by-step explanation:

The probability, in this case, has to be calculated using the sum rule because the events are independent. 

P = P(men) + P(non-fiction) - P(men non-fiction); where P is the probability. It means the probability that the random book was written by a man plus the probability that the random book was non-fiction minus the probability that the random book was written by a man who writes non-fiction. The probability that the random book was written by a man who writes non-fiction has to be subtracted, if not you will be duplicating it. 

Facts:

P(men) = 60% = 99/165

P(non-fiction) = 40% = 66/165

P(men non-fiction) = 40/165

P = P(men) + P(non-fiction) – P(men non-fiction)

P = 99/165 + 66/165 – 40/165

P = 125/165

P = 0.758 or 75.8%