Question

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

• A. 0
• B. $\frac{1}{6}$
• C. $\frac{1}{12}$
• D. $\frac{1}{36}$

Hint:

"Even prime number" is a classic trick phrase in probability questions. Always remember that 2 is the only even prime number. 1 is neither prime nor composite.

Answer 1

The Correct Option is D

To determine the probability of obtaining an even prime number on each die when a pair of dice is rolled, we need to identify which numbers on a die are even and prime. A standard die has six faces, numbered from 1 to 6.

First, let's identify the even numbers on a standard die:

• 2
• 4
• 6

Next, among these even numbers, let's determine which ones are prime numbers. A prime number is a number that has only two distinct positive divisors: 1 and itself.

• 2 is an even prime number since its only divisors are 1 and 2.
• 4 is not a prime number since its divisors are 1, 2, and 4.
• 6 is not a prime number since its divisors are 1, 2, 3, and 6.

Thus, the only even prime number on a die is 2.

We are asked to find the probability that each die shows an even prime number, which is 2. Since each roll of the die is independent, the probability of rolling a 2 on one die is \(\frac{1}{6}\) because there are 6 possible outcomes.

Therefore, the probability of rolling a 2 on both dice is obtained by multiplying the probabilities from each die:

\[\text{Probability} = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\]

Hence, the probability of obtaining an even prime number (which is 2) on each die when a pair of dice is rolled is \(\frac{1}{36}\).