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)

$\frac {13} {18}$

Answer 2

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 $=P\left(E'\right)=1-P(E)$
$=1-\frac{10}{36}$
$=\frac{26}{36}=\frac{13}{18}$