Question

Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{9}$
• D. $\frac{5}{9}$

Answer 1

The correct option is C $\frac{4}{9}$

Let the probability of an odd numbered face coming up be $x$. So, the probability of an even numbered face coming up is $2x$.

As there are $3$ even and $3$ odd faces, $3x+3\times 2x=1⟹x=\frac{1}{9}$

Now, the prime numbers from the mix are $2,3$ and $5$.

$\therefore$ probability of prime number showing up $=P\left(2\right)+P\left(3\right)+P\left(5\right)=\frac{2+1+1}{9}=\frac{4}{9}$