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A and B are two groups of books, Group A consists of 9 science and 5 engineering books and the group B consists of 6 science and 7 engineering books. When an unbiased die is rolled, if 2 or 5 turns up, a book is selected at random from the group A, otherwise a book is selected at random from the B group. When an unbiased die is rolled, the probability of selecting a science book is

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$\frac{13}{36}$

$\frac{34}{35}$

$\frac{20}{39}$

$\frac{13}{24}$

answer is C.

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Detailed Solution

	A	B
S	8	6
E	5	7

$E_{1} =$ Selected bag A when a die is thrown 2 or 5 turn up

$E_{2} =$ Selected bag B when a die thrown 1 or 3 or 4 or 6 turn up

$P (E_{1}) = \frac{2}{6} P (E_{2}) = \frac{4}{6}$

A=Selecting Science book

$\begin{array}{rcl} P (\frac{A}{E_{1}}) & = & \frac{8}{13} P (\frac{A}{E_{2}}) = \frac{6}{13} \\ P (A) & = & \frac{2}{6} \times \frac{8}{13} + \frac{4}{6} \times \frac{6}{13} \\ = & \frac{8 + 12}{39} = \frac{20}{39} \end{array}$

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