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. The probability that the sum of the two numbers thrown is even is:

• A. $\frac{4}{9}$
• B. $\frac{4}{3}$
• C. $\frac{5}{9}$
• D. $\frac{7}{9}$

Answer 1

The correct option is C $\frac{5}{9}$

Let the probability of getting an odd number be $p$, and the probability of getting an even number be $2p$
$\therefore p+2p=1$
$\Rightarrow 3p=1$
$\Rightarrow p=\frac{1}{3}$
Hence, the probability of odd number $=\frac{1}{3}$
and probability for even number $=2p=\frac{2}{3}$
Now sum of two numbers is even means either both are odd or both are even.
$\therefore$ Required probability
$=\frac{1}{3}\times \frac{1}{3}+\frac{2}{3}\times \frac{2}{3}=\frac{1}{9}+\frac{4}{9}=\frac{5}{9}$