Question

Two dice are rolled simultaneously . Find the probability of

A) getting a sum more than $10$

B) getting a sum more than $6$ and a multiple of $3$

Answer 1

When two dice are thrown then the total number of outcomes are $n\left(S\right)=6\times 6$ as each die gives $6$ possible outcomes.
$\therefore n\left(S\right)=36$

A)
Possible combinations of sum grater than $10$ are
$E=\left\{\right(6,5),(6,5),(6,6\left)\right\}$
$\Rightarrow n\left(E\right)=3$
Therefore, probability getting a sum more than $10=\frac{n\left(E\right)}{n\left(S\right)}$
$=\frac{3}{36}$
$=\frac{1}{12}$
B)
Possible combination of sum greater than $6$ and multiple of $3$ is
$F=\left\{\right(6,6\left)\right(6,3\left)\right(3,6\left)\right\}$
$\Rightarrow n\left(F\right)=3$
Therefore, probability of getting a sum more than $6$ and a multiple of $3=\frac{3}{36}$
$=\frac{1}{12}$