In two dice game, the player take turns to roll both dice, they can roll as many times as they want in one turn. A player scores the sum of the two dice thrown and gradually reaches a higher score as they continue to roll. If a single number 1 is thrown on either die, the score for that whole turn is lost. Two dice are thrown simultaneously.

What is the probability of getting the sum as an even number ?

Options

A. `(3)/(4)`
B. `(1)/(2)`
C. `(1)/(4)`
D. `(5)/(8)`

Answer

D

Explanation

All possible outcome are given as below :
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Number of all possible outcomes in all case,
`n(S)=6xx6=36`
Favourable outcome are {2, 4, 6, 8, 10, 12}. We may get as follows
`{(1, 1), (1, 3), (3, 1), (2, 2), (1, 5), (5, 1), (2, 4), (4, 2), (3, 3), (2, 6), (6, 2), (3, 5), (5, 3), (4, 4), (6, 4), (4, 6), (5, 5), (6, 6)}`
Thus number of favourable outcomes,
`n(E_(1))=18`
P(sum as an even number),
`P(E_(1))=(n(E_(1)))/(n(S))=(18)/(36)=(1)/(2)`
Thus (d) is correct option.