Question

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

• A. $\frac{1}{36}$
• B. $\frac{1}{6}$
• C. $\frac{1}{18}$
• D. $\frac{1}{4}$

Hint:

The only even prime number is 2. Hence both dice must show 2.

Answer 1

The Correct Option is A

Step 1: Identify the even prime number.
Prime numbers are numbers greater than 1 having exactly two factors. Among all prime numbers, the only even prime number is \[ 2 \] Thus each die must show the number \(2\).

Step 2: Determine the total possible outcomes.
When two dice are rolled, the total number of possible outcomes is \[ 6 \times 6 = 36 \]
Step 3: Determine favourable outcomes.
To obtain an even prime number on each die: First die = \(2\) Second die = \(2\) Thus the favourable outcome is \[ (2,2) \] Hence the number of favourable outcomes is \[ 1 \]
Step 4: Compute the probability.
\[ P(\text{both even prime}) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} \] \[ = \frac{1}{36} \]
Step 5: Conclusion.
Thus the probability that both dice show an even prime number is \[ \frac{1}{36} \] Final Answer: $\boxed{\frac{1}{36}}$