Question

A pair of the die is thrown. Find the probability of getting a sum of $10$ or more, if $5$ appears on the first die.

Answer 1

In throwing a dice, total possible outcomes $=1,2,3,4,5,6$

So, $n\left(S\right)=6$

For two dice, $n\left(S\right)=6\times 6=36$

Favorable cases where the sum is $10$ or more with $5$ on $1st$ die $=(5,5),(5,6)$

Event of getting the sum is $10$ or more with $5$ on 1st die $=n\left(E\right)=2$

Hence, the probability of getting a sum of $10$ or more with $5$ on 1st die $=n\left(E\right)/n\left(S\right)=2/36=1/18$