Question

What is the probability that a randomly selected reference book is hardcover?

0.25
0.4
0.6
0.75

Answer 1

0.4

Explanation:

Answer 2

Answer: The correct option is (B) 0.4.

Step-by-step explanation: We are given to find the probability that a randomly selected reference book is hardcover.

Let, S denote the sample space for the experiment of selecting a book.

Then, n(S) = 60.

Let A denote the event that the selected book is is a reference one and B denote the event that the selected book is a hardcover.

Then, according to the given information, we have

`n(A)=25,~~~n(B)=40,~~~n(A\cap B)=10.`

So,

`P(A)=(n(A))/(n(S))=(25)/(60)=(5)/(12),\\\\\\P(B)=(n(B))/(n(S))=(40)/(60)=(2)/(3)\\\\\\P(A\cap B)=(n(A\cap B))/(n(S))=(10)/(60)=(1)/(6).`

Therefore, the probability that a randomly selected reference book is hardcover is equal to the conditional probability of event B given A.

That is, the required probability is

`P(B/A)=(P(B\cap A))/(P(A))=((1)/(6))/((5)/(12))=(1)/(6)*(12)/(5)=(5)/(5)=0.4.`

Option (B) is correct.