If three standard six-sided dice are rolled simultaneously, what is the probability that all three dice display the same number?

Explanation

To find the probability that all three dice show identical numbers, consider the possible outcomes. Each die has 6 faces, so total possible outcomes when rolling three dice is 6 × 6 × 6 = 216. The favorable outcomes are the triplets where all dice show the same face: (1,1,1), (2,2,2), ..., (6,6,6), totaling 6 outcomes. Therefore, the probability is 6 divided by 216, which simplifies to 1/36.