Question

In a simultaneously throw of a pair of dice, the probability of getting a total more than $7$ is?

• A. $\frac{7}{12}$
• B. $\frac{5}{36}$
• C. $\frac{5}{12}$
• D. $\frac{7}{36}$

Answer 1

The correct option is C $\frac{5}{12}$

Sample space $S=\left\{\right(1,1),(1,2),(1,3),(1,4)\dots (6,6\left)\right\}$

$n\left(S\right)=36$

Sum $=\{8,9,10,11,12\}$

$E=\left\{\right(4,4),(5,3),(3,5),(6,2),(2,6),(3,6),(6,3),(4,5),(5,4),(5,5),(6,4),(4,6),(5,6),(6,5),(6,6\left)\right\}$

$n\left(E\right)=15$
Prob$=\frac{15}{36}=\frac{5}{12}$.