select the correct answer.\nyour personal library contains books written by 165 authors. 60% of the authors…

select the correct answer.\nyour 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?\na. $\frac{3}{5}$\nb. $\frac{58}{165}$\nc. $\frac{25}{33}$\nd. $\frac{2}{5}$

select the correct answer.\nyour 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?\na. $\frac{3}{5}$\nb. $\frac{58}{165}$\nc. $\frac{25}{33}$\nd. $\frac{2}{5}$

Answer

Answer:

C. $\frac{25}{33}$

Explanation:

Step1: Calculate number of male authors

The total number of authors is $n = 165$. The number of male authors is $0.6\times165=99$.

Step2: Calculate number of non - fiction authors

The number of authors who write only non - fiction is $0.4\times165 = 66$.

Step3: Calculate number of male non - fiction authors

Given that the number of male non - fiction authors is 40.

Step4: Use the addition rule of probability

The probability of an event $A$ or $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that a book is written by a non - fiction author and $B$ be the event that a book is written by a man. Then $P(A)=\frac{66}{165}$, $P(B)=\frac{99}{165}$ and $P(A\cap B)=\frac{40}{165}$. [ \begin{align*} P(A\cup B)&=\frac{66 + 99-40}{165}\ &=\frac{125}{165}\ &=\frac{25}{33} \end{align*} ]