Question

If a pair of dice is thrown, the probability of getting an even prime number on each die is __________.

Hint:

The only even prime number is \( 2 \), so when rolling dice, the probability of both dice showing \( 2 \) is \( \frac{1}{36} \).

Answer 1

Step 1: An even prime number is a number that is both even and prime. The only even prime number is \( 2 \). 

Step 2: Each die has the numbers \( 1, 2, 3, 4, 5, 6 \). For the condition to be satisfied (getting an even prime number on each die), both dice must show the number \( 2 \). 

Step 3: The total number of possible outcomes when two dice are thrown is: \[ 6 \times 6 = 36. \] 

Step 4: The only favorable outcome is when both dice show \( 2 \), so there is exactly one favorable outcome. 

Step 5: Therefore, the probability of getting an even prime number on each die is: \[ \frac{1}{36}. \] Thus, the correct answer is \( \frac{1}{36} \).