Question

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

Answer 1

Answer: The required probability is 22%.

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)

`=0.6* 0.3+0.4* 0.1\\\\=0.18+0.04\\\\=0.22\\\\=22\%`

Hence, the required probability is 22%.