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

∵ Probability for odd = p
∴ Probability for even = 2p
∵ p + 2p = 1
⇒ 3p = 1
⇒ p = 1/3
∴ Probability for odd = 1/3, Probability for even = 2/3.
Sum of two nos. is even means either both are odd or both are even
∴ Reqd. probability = 1/3 x 1/3 + 2/3 x 2/3 = 1/9 + 4/9 = 5/9
[ ∵ die is thrown twice ]