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Sagot :
To solve the problem, we will analyze the information step-by-step:
1. Total Number of Authors: There are 165 authors.
2. Percentage of Male Authors: [tex]\(60\%\)[/tex] of the authors are men.
- Number of male authors:
[tex]\[ \text{Number of male authors} = 165 \times 0.60 = 99 \][/tex]
3. Percentage of Authors Who Write Only Nonfiction: [tex]\(40\%\)[/tex] of the authors write only nonfiction.
- Number of nonfiction authors:
[tex]\[ \text{Number of nonfiction authors} = 165 \times 0.40 = 66 \][/tex]
4. Number of Male Authors Who Write Only Nonfiction:
- Given that 40 male authors write only nonfiction.
5. Number of Male Authors Who Write Other Works:
- The total number of male authors is 99, and 40 write only nonfiction. Therefore, the number of male authors who write other works is:
[tex]\[ \text{Number of male authors who write other works} = 99 - 40 = 59 \][/tex]
6. Number of Nonfiction Authors Who Are Not Male:
- There are 66 nonfiction authors in total. Out of these, 40 are male.
[tex]\[ \text{Number of nonfiction authors who are not male} = 66 - 40 = 26 \][/tex]
_We are interested in finding 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._
7. Number of Favorable Cases:
- Books written by male authors who write only nonfiction: 40
- Books written by male authors who write other works: 59
- Books written by nonfiction authors who are not male: 26
The number of favorable cases is:
[tex]\[ \text{Total favorable cases} = 40 + 59 + 26 = 125 \][/tex]
8. Calculate the Probability:
- The probability that a randomly selected book is either written by an author who writes only nonfiction or written by a man is the number of favorable cases divided by the total number of authors:
[tex]\[ \text{Probability} = \frac{\text{Total favorable cases}}{\text{Total number of authors}} = \frac{125}{165} \][/tex]
9. Simplify the Fraction:
[tex]\[ \frac{125}{165} \approx 0.7576 \quad \text{(a recurring decimal which is also approximately)} \quad \frac{25}{33} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\frac{25}{33}} \][/tex]
Therefore, the correct answer is C.
1. Total Number of Authors: There are 165 authors.
2. Percentage of Male Authors: [tex]\(60\%\)[/tex] of the authors are men.
- Number of male authors:
[tex]\[ \text{Number of male authors} = 165 \times 0.60 = 99 \][/tex]
3. Percentage of Authors Who Write Only Nonfiction: [tex]\(40\%\)[/tex] of the authors write only nonfiction.
- Number of nonfiction authors:
[tex]\[ \text{Number of nonfiction authors} = 165 \times 0.40 = 66 \][/tex]
4. Number of Male Authors Who Write Only Nonfiction:
- Given that 40 male authors write only nonfiction.
5. Number of Male Authors Who Write Other Works:
- The total number of male authors is 99, and 40 write only nonfiction. Therefore, the number of male authors who write other works is:
[tex]\[ \text{Number of male authors who write other works} = 99 - 40 = 59 \][/tex]
6. Number of Nonfiction Authors Who Are Not Male:
- There are 66 nonfiction authors in total. Out of these, 40 are male.
[tex]\[ \text{Number of nonfiction authors who are not male} = 66 - 40 = 26 \][/tex]
_We are interested in finding 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._
7. Number of Favorable Cases:
- Books written by male authors who write only nonfiction: 40
- Books written by male authors who write other works: 59
- Books written by nonfiction authors who are not male: 26
The number of favorable cases is:
[tex]\[ \text{Total favorable cases} = 40 + 59 + 26 = 125 \][/tex]
8. Calculate the Probability:
- The probability that a randomly selected book is either written by an author who writes only nonfiction or written by a man is the number of favorable cases divided by the total number of authors:
[tex]\[ \text{Probability} = \frac{\text{Total favorable cases}}{\text{Total number of authors}} = \frac{125}{165} \][/tex]
9. Simplify the Fraction:
[tex]\[ \frac{125}{165} \approx 0.7576 \quad \text{(a recurring decimal which is also approximately)} \quad \frac{25}{33} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\frac{25}{33}} \][/tex]
Therefore, the correct answer is C.
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