Let's break down the solution step-by-step:
1. Total number of authors: 165
2. Number of male authors:
[tex]\[
0.60 \times 165 = 99
\][/tex]
3. Number of authors who write only nonfiction:
[tex]\[
0.40 \times 165 = 66
\][/tex]
4. Number of male authors who write only nonfiction: 40 (given)
5. Number of female authors who write only nonfiction:
[tex]\[
66 - 40 = 26
\][/tex]
6. Number of male authors who write fiction:
[tex]\[
99 - 40 = 59
\][/tex]
7. Number of female authors:
[tex]\[
165 - 99 = 66
\][/tex]
8. Number of female authors who write fiction:
[tex]\[
66 - 26 = 40
\][/tex]
Next, we determine the total number of authors who write nonfiction or are men.
9. Total number of authors who write nonfiction: 66 (given by calculation)
10. Total number of authors who are men: 99 (calculated above)
Now, to avoid double-counting the male authors who write only nonfiction, we need to subtract them once from the total of 99 male authors and 66 nonfiction authors:
11. Total number of authors who write nonfiction or are men:
[tex]\[
66 + 99 - 40 = 125
\][/tex]
12. Probability that a randomly picked book is either written by an author who writes only nonfiction or a male author:
[tex]\[
\frac{125}{165}
\][/tex]
Simplify this fraction:
13. [tex]\(\frac{125}{165} = 0.7575757575757576 \approx \frac{25}{33}\)[/tex]
Thus, the probability that a randomly picked book is either written by an author who writes only nonfiction or a male author is:
Answer: C. [tex]\(\frac{25}{33}\)[/tex]
