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

# 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

1. A

5/36

2. B

1/6

3. C

5/18

4. D

13/18

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### Solution:

Total number of outcomes in sample space, n(S)=6x6=36
Let E = Event of getting maximum sum of numbers on two dice is 5
= (1, 1), (1, 2), (2, 1), (1,3), (3, 1), (2, 2),(1, 4), (4, 1), (2, 3), (3, 2))
$\therefore$ n(E) = 10
$\therefore$ P (the maximum sum of numbers on two dice is 5) $=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{10}{36}=\frac{5}{18}$

$\therefore$P (sum of number on two dice i8 more that 5) = 1 - P (the maximum sum on the two die is 5)$=1-\frac{5}{18}=\frac{13}{18}$

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