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
[tex]n(A)=25,~~~n(B)=40,~~~n(A\cap B)=10.[/tex]
So,
[tex]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}.[/tex]
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
[tex]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.[/tex]
Option (B) is correct.
