Respuesta :
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.
Answer:
Option: C is the correct answer.
C) 25/33
Step-by-step 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:
[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]
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,
[tex]P(A\bigcup B)=\dfrac{66}{165}+\dfrac{99}{165}-\dfrac{40}{165}\\\\\\P(A\bigcup B)=\dfrac{66+99-40}{165}\\\\\\P(A\bigcup B)=\dfrac{125}{165}\\\\\\P(A\bigcup B)=\dfrac{25}{33}[/tex]
Hence, the probability is:
C) 25/33