Question

Choose the correct answer.
The probability of obtaining an even prime number on each die when a pair of dice is rolled is
(a) zero (b) $\frac{1}{3}$ (c) $\frac{1}{12}$ (d) $\frac{1}{36}$

Answer 1

When a pair of dice is rolled once, the sample space contains $6\times 6=36$ elements.
i.e., n(S) = 36
The only even prime number is 2.
Let E be the event of getting an even prime numbner on each die, E = (2, 2)
i.e., n(E) = 1
Required probability = P (an even prime on each die)
$=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1}{36}$