Answer to Question #168344 in Statistics and Probability for Bikram Chaudhary

Question

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

Answer 1

$P(odd) = p$

$P(even) = 2p$

$p + 2p = 1\implies p=\frac{1}{3}$

Thus $P(odd) = \frac{1}{3}$ $P(even) = \frac{2}{3}$

The sum of the two number thrown is even when both of them are either even or both of them are odd, therefore:

$P(even \ sum)=\frac{1}{3}\cdot\frac{1}{3}+\frac{2}{3}\cdot\frac{2}{3}=\frac{5}{9}$

Answer: $\frac{5}{9}$