Question:
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
(A) 0
(B) $\frac{1}{3}$
(C) $\frac{1}{12}$
(D) $\frac{1}{36}$
Solution:
When two dice are rolled, the number of outcomes is 36.
The only even prime number is 2.
Let E be the event of getting an even prime number on each die.
$\therefore E=\{(2,2)\}$
$\Rightarrow P(E)=\frac{1}{36}$
Therefore, the correct answer is D.
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