Question

Three dice are thrown at the same time. Find the probability of getting three twos, if it is known that sum of the number on three dice is six.

Answer 1

Three dice are thrown simultaneously.

There are $216$ element in the total sample space.

Let us define an element $A$ by assuming the numbers on the dice is $6$

$A=(2,2,2),(2,1,3),(2,3,1),(1,3,2),(1,2,3),(1,1,4),(4,1,1),(1,4,1),(3,1,2),(3,2,1)$

$B=$ getting a number $3$ in all $3$ dice $=(2,2,2)$

Since it is given that the event $A$ has already occured.

i.e., the sum of the numbers on each die is $6$

We have $10$ cases out of which only one $(2,2,2)$ is favourable to us.

$\therefore P\left(B\right)=\frac{1}{10}$