Question

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled on each die is:

• A. \( \frac{1}{36} \)
• B. \( \frac{1}{12} \)
• C. \( \frac{1}{8} \)
• D. \( \frac{1}{4} \)

Hint:

When calculating the probability of independent events occurring simultaneously, multiply the probabilities of the individual events.

Answer 1

The Correct Option is D

A cube-shaped die has 6 faces, and the even numbers on the die are 2, 4, and 6. Therefore, the probability of rolling an even number on a single die is: \[ P(\text{even on one die}) = \frac{3}{6} = \frac{1}{2}. \] Since the dice are rolled simultaneously, the probability that both dice show an even number is the product of the individual probabilities: \[ P(\text{even on both dice}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}. \] Final Answer: \[ \boxed{\frac{1}{4}}. \]