Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is

$\frac{1}{5}$

The correct answer is Option (3) → $\frac{1}{5}$ ##

Let $E_1 =$ Event that the sum of numbers on the dice was less than 6

and $E_2 =$ Event that the sum of numbers on the dice is 3.

$∴E_1 = \{(1, 4), (4, 1), (2, 3), (3, 2), (2, 2), (1, 3), (3, 1), (1, 2), (2, 1), (1, 1)\}$

$\Rightarrow n(E_1) = 10$

and $E_2 = \{(1, 2), (2, 1)\} \Rightarrow n(E_2) = 2$

$∴E_1 \cap E_2 = \{(1, 2), (2, 1)\} \Rightarrow n(E_1 \cap E_2) = 2$

$∴P(E_2 \mid E_1) = \frac{P(E_1 \cap E_2)}{P(E_1)} = \frac{2/36}{10/36} = \frac{2}{10} = \frac{1}{5}$