A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7. The probability that the number 3 has appeared atleast once, is

Options

A. `(1)/(5)`
B. `(1)/(2)`
C. `(1)/(3)`
D. `(1)/(4)`

Answer

C

Explanation

Sum of numbers appearing on the dice is 7.
`S={(1, 6), (6, 1), (2, 5), (2, 5), (5, 2), (3, 4), (4, 3)}`
`therefore n(S) = 6`
Let E = Event of getting 3 atleast once
`therefore n(E )=2`
`therefore` Required probability `=(n(E ))/(n(S))=(2)/(6)=(1)/(3)`