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?

A) 3/5
B) 58/165
C) 25/33
D) 2/5

Answer 1

Option: C is the correct answer.

C) 25/33

Explanation:

Let A denote the event that the novel is written by a author who writes non-fiction .

and B denote the event that the book is written by a man.

A∩B denotes the man author who writes non-fiction.

Let P denotes the probability of an event.

Hence, from the given information we have:

40% of the authors write only nonfiction works.

This means that out of 165 authors 40% (which is 0.4) writes non-fiction.

i.e. 0.4×165=66 authors

i.e. A=66

Also, Number of novels written by man=99

( Since, 60% of the authors are men.

i.e. B=0.6×165=99 )

Hence, B=99

Also, 40 of the male authors write only nonfiction works.

i.e. A∩B=40

Hence,

P(A)=66/165

P(B)=99/165

P(A∩B)=40/165

Hence, we know that:

`P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)`

where P(A∪B) 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.

Hence,

`P(A\bigcup B)=(66)/(165)+(99)/(165)-(40)/(165)\\\\\\P(A\bigcup B)=(66+99-40)/(165)\\\\\\P(A\bigcup B)=(125)/(165)\\\\\\P(A\bigcup B)=(25)/(33)`

Hence, the probability is:

C) 25/33

Answer 2

The probabbility 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 equal to [40% of 165 + 60% of 165 - 40] / 165. The sum of the individual probabilities is taken and subtracted by the probability of the two events. The answer is c. 25/33.