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 numbers thrown is even?

Answer 1

$\because$ probability for odd $=p$

$\therefore$ probability for even $=2p$

$\because$ $p+2p=1$

$\Rightarrow 3p=1$

$\Rightarrow p=\frac{1}{3}$

$\therefore$ probability for odd $=\frac{1}{3}$ $,$ probability for even$=\frac{2}{3}$

Sum of two no. is even means either both are odd or both are even

$\therefore$ required probability $=\frac{1}{3}\times \frac{1}{3}+\frac{2}{3}\times \frac{2}{3}=\frac{1}{9}+\frac{4}{9}=\frac{5}{9}$