Question

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

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{3}$
• D. $\frac{5}{9}$

Answer 1

The correct option is D

$\frac{5}{9}$

Explanation for the correct option:

Step 1. Let the probability for odd number $=p$

And probability for even number $=2p$

$\Rightarrow p+2p=1$ $...\left[Since,P\left(E\right)+P\left(\overline{E}\right)=1\right]$

$\Rightarrow 3p=1$

$\Rightarrow p=\frac{1}{3}$​

Therefore, probability for odd number $=\frac{1}{3}$​ , probability for even number $=2p=\frac{2}{3}$

Step 2. Sum of two numbers is even means that either both numbers are odd or both are even

Thus, The required probability $=\frac{1}{3}\times \frac{1}{3}+\frac{2}{3}\times \frac{2}{3}$

$=\frac{1}{9}+\frac{4}{9}=\frac{\mathbf{5}}{\mathbf{9}}$

Hence, Option ‘D’ is Correct.