Question

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

Answer 1

Answer:

0.4

Step-by-step 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,

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{25}{60}=\dfrac{5}{12},\\\\\\P(B)=\dfrac{n(B)}{n(S)}=\dfrac{40}{60}=\dfrac{2}{3}\\\\\\P(A\cap B)=\dfrac{n(A\cap B)}{n(S)}=\dfrac{10}{60}=\dfrac{1}{6}.$

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

$P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\frac{1}{6}}{\frac{5}{12}}=\dfrac{1}{6}\times\dfrac{12}{5}=\dfrac{5}{5}=0.4.$

Option (B) is correct.