To find the correct probability, let's break down the problem step-by-step:
1. Total Authors: The total number of authors is 165.
2. Percentage of Men: 60% of the authors are men. This means the number of male authors is:
[tex]\[
165 \times 0.60 = 99 \text{ men}
\][/tex]
3. Percentage of Nonfiction Authors: 40% of the authors write only nonfiction. This means the number of nonfiction authors is:
[tex]\[
165 \times 0.40 = 66 \text{ nonfiction authors}
\][/tex]
4. Male Nonfiction Authors: We know that 40 male authors write only nonfiction.
5. Female Authors: Since there are 99 male authors, the number of female authors is:
[tex]\[
165 - 99 = 66 \text{ women}
\][/tex]
6. Female Nonfiction Authors: Out of 66 nonfiction authors, 40 are men. So, the number of nonfiction authors who are women is:
[tex]\[
66 - 40 = 26 \text{ female nonfiction authors}
\][/tex]
7. Male Fiction Authors: The number of men who write fiction only is:
[tex]\[
99 - 40 = 59 \text{ male fiction authors}
\][/tex]
8. Female Fiction Authors: The number of women who write fiction only is:
[tex]\[
66 - 26 = 40 \text{ female fiction authors}
\][/tex]
9. Nonfiction or Male Authors: To find out how many authors write either only nonfiction or are men, we sum up:
- The number of nonfiction authors (men and women): 66
- The number of male fiction authors: 59
So, the total number is:
[tex]\[
66 + 59 = 125 \text{ authors}
\][/tex]
10. Probability: The probability that a book picked at random is either a work by an author who writes only nonfiction or by a male author is:
[tex]\[
\frac{125}{165}
\][/tex]
To simplify the fraction \(\frac{125}{165}\), we can divide the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{125 \div 5}{165 \div 5} = \frac{25}{33}
\][/tex]
Thus, the correct answer is:
C. [tex]\(\frac{25}{33}\)[/tex]
