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

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

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

$\Rightarrow$ $n\left( {{E_1}} \right) = 10$

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

$\therefore$ Required probability $= \frac{2}{{10}} = \frac{1}{5}$