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The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

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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