Two dice are thrown. If it is known that the sum of the numbers on the dice was less than `6`, the probability of getting a sum `3` is

Options

A. a) `1/18`
B. a) `5/18`
C. c) `1/5`
D. d) `2/5`

Answer

c) `1/5`

Explanation

Let,


`E_1 =` Sum of numbers on the dice was `lt 6`


`E_2 =` Sum of numbers on the dice is `3`


`E_1 = {(1,4), (4,1), (2,3), (3,2), (2,2), (1,3), (3,1), (1,2), (2,1), (1,1)}`


`n(E_1)=10`


`E_2={(1,2),(2,1)}`


`n(E_2)=2`


Required probability `=2/10=1/5`