Probability — Class 12 Maths Solution

On a throw of three dice, we have sample space $[n(S)] = {6^3} = 216$

Let ${E_1}$ is the event when the sum of numbers on the dice was six and ${E_2}$ is the event when three two's occurs.

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

$(2,2,2),(2,3,1),(3,1,2),(3,2,1),(4,1,1)\}$
$\Rightarrow$ $n\left( {{E_1}} \right) = 10$

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

Also, $\left( {{E_1} \cap {E_2}} \right) = 1$

$\therefore$ $P\left( {{E_2}/{E_1}} \right) = \frac{{\bar P \cdot \left( {{E_1} \cap {E_2}} \right)}}{{P\left( {{E_1}} \right)}} = \frac{{1/216}}{{10/216}} = \frac{1}{{10}}$