A and B are two groups of books. Group A cons | vedclass

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(C) Let $E$ be the event of selecting a science book.Let $A$ be the event of selecting a book from group $A$, and $B$ be the event of selecting a book

Vedclass · Accepted Answer

$\frac{20}{39}$

Vedclass · Answer

(C) Let $E$ be the event of selecting a science book.Let $A$ be the event of selecting a book from group $A$, and $B$ be the event of selecting a book from group $B$.The probability of getting $2$ or $5$ on a die is $P(A) = \frac{2}{6} = \frac{1}{3}$.The probability of not getting $2$ or $5$ is $P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.In group $A$, there are $8$ science and $5$ engineering books, total $13$ books. So, $P(E|A) = \frac{8}{13}$.In group $B$, there are $6$ science and $7$ engineering books, total $13$ books. So, $P(E|B) = \frac{6}{13}$.Using the law of total probability:$P(E) = P(A) 	imes P(E|A) + P(B) 	imes P(E|B)$$P(E) = \frac{1}{3} 	imes \frac{8}{13} + \frac{2}{3} 	imes \frac{6}{13}$$P(E) = \frac{8}{39} + \frac{12}{39} = \frac{20}{39}$

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