Question

In a simultaneous throw of a pair of dice, find the probability of getting a total more than $7$.

Answer 1

Find the probability of the event of throwing two dice at a time and getting a total more than $7$:

Sample space of the event (throwing two dice at a time), the total possible outcomes are $\left(S\right)=6\times 6=36$.

The total number of possible outcomes of the event is $n\left(S\right)=36$

Outcomes favoring the event (where we get a sum more than 7) are $=\left\{\right(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6\left)\right\}$

Total number of favorable outcomes $n\left(E\right)=15$

We know, probability of an event $=\frac{numberoffavorableoutcomes}{totalnumberofoutcomes}$

Probability of getting a sum more than $7=\frac{n\left(E\right)}{n\left(S\right)}$

$$\begin{gathered} =\frac{15}{36} \\ =\frac{5}{12} \end{gathered}$$

Hence, probability of getting a sum more than $7is\frac{5}{12}$.