30% of the library books in the fiction are worn and need replacement.10% of the nonfiction holdings are worn. The library's holdings are 60% fiction and 40% nonfiction. Find the probability that a book chosen at random from this library is worn and needs replacement

The required probability is 22%.

Step-by-step explanation:

Since we have given that

Percentage of the library books in the fiction are worn and need replacement = 30%

Probability of non fiction holdings are worn = 10%

Probability of books are fiction = 60%

Probability of books are non fiction = 40%

So, Probability that a book chosen at random from this library is worn and needs replacement is given by

P(F).P(F∩W)+P(F').P(F'∩W)

Hence, the required probability is 22%.