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. none of these

Answer 1

The correct option is E

none of these

Explanation for the correct answer:

Finding the probability that the sum of the numbers which come up on the dice to be more than $5$ :

Given, that two dice are thrown simultaneously,

Then, the total number of sample spaces is $36$

The total favorable outcome is that the sum of the numbers which come up on the dice is more than $5$

So,

Favorable outcomes $$\begin{gathered} =\left\{(1,5),(1,6),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1), \\ (5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\right\} \end{gathered}$$

Therefore, the required probability $=\frac{Favorableoutcomes}{samplespace}$

$$\begin{gathered} =\frac{26}{36} \\ =\frac{13}{18} \end{gathered}$$

Hence, the correct option is D.