When rolling two fair six-sided dice, we want to determine the probability that the numbers on both dice match.
There are a total of 6 possible outcomes for the first die (numbers 1 through 6) and 6 possible outcomes for the second die, resulting in:
- Total possible outcomes = 6 * 6 = 36
For the two dice to show the same number, the possible matching pairs are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)
This gives us a total of 6 favorable outcomes where both dice match. The probability is then calculated by dividing the number of favorable outcomes by the total number of outcomes:
- Probability = Favorable outcomes / Total outcomes = 6 / 36
This simplifies to:
- Probability = 1 / 6
Therefore, the probability that the two dice will show the same number is 1/6.