If two dice are thrown simultaneously, then the probability that the sum of the numbers which come upon the dice to be more than 5 is

Options

A. `(5)/(36)`
B. `(1)/(6)`
C. `(13)/(18)`
D. `(7)/(18)`

Answer

C

Explanation

Total number of outcomes in sample space,
`n(S)=6xx6=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)
`=(n(E ))/(n(S))=(10)/(36)=(5)/(18)`
`therefore` P (sum of number on two dice is more than 5)
= 1 - P (the maximum sum of numbers on two dice is 5)
`= 1 -(5)/(18)=(13)/(18)`