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. $\frac {13} {18}$

Answer 1

Answer: (D)

Let $E$ be the event getting sum less than equal to 5 .
Then,
$E=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2), (2,3),(3,1),(3,2),(4,1)\}$
$\therefore P(E)=\frac{10}{36} $
So, required probability $ =P\left(E'\right)=1-P(E) $
$ =1-\frac{10}{36} $
$ =\frac{26}{36}=\frac{13}{18}$