Question

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than $5$ is

• A. $\frac{5}{36}$
• B. $\frac{1}{6}$
• C. $\frac{5}{18}$
• D. $\frac{7}{18}$
• E. $\frac{13}{18}$

Answer 1

The correct option is E $\frac{13}{18}$

Total number of sample space,
$n\left(S\right)=6\times 6=36$
Let $E=$ Event of getting the sum of two dices is more than $5$
$=\left\{\right(1,5),(1,6),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),$

$(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$
$\therefore n\left(E\right)=26$
Probability (sum of two dices is more than $5$)
$=\frac{n\left(E\right)}{n\left(S\right)}=\frac{26}{36}=\frac{13}{18}$

Hence, option E is correct.