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

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)  (5 /36) (B)  (1 /6) (C)  (5 /18) (D)  (13 /18)

Tardigrade Admin · Accepted Answer

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) ∴ P(E)=(10/36) So, required probability =P(E')=1-P(E) =1-(10/36) =(26/36)=(13/18)

Q. 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

$\frac{5}{36}$

$\frac{1}{6}$

$\frac{5}{18}$

$\frac{13}{18}$

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

Q. 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

365​

61​

185​

1813​