In a library, 70% of the books are in English and 30% are in Hindi. 10% of the English books and 5% of the Hindi books are damaged. A book is chosen at random from the library. The probability that it is damaged is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.085
Let \(E_1\) and \(E_2\) be the events that the book is in English and in Hindi, and let D be the event that it is damaged.
\(P(E_1) = 0.7,\quad P(E_2) = 0.3\)
\(P(D|E_1) = 0.10,\quad P(D|E_2) = 0.05\)
The two kinds of books cover the whole library, so by the theorem of total probability:
\(P(D) = 0.7\times 0.10 + 0.3\times 0.05\)
\(P(D) = 0.070 + 0.015 = 0.085\)