A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is

Options

A. `(4)/(9)`
B. `(5)/(9)`
C. `(1)/(9)`
D. None of these

Answer

B

Explanation

let p be the probability of getting an even number and q that of an odd number in a single throw of a dice.
Then , `p=2q and p+q=1 `
`implies p=(2)/(3),q=(1)/(3)`
Required probability
=Probability that an odd number appears both times + Probability that an even number appears both times
`=""^(2)C_(0)(1/3)^(2) + ""^(2)C_(2)(2/3)^(2)=1/9 + 4/9 =5/9`