To find the probability of both six-sided dice showing a one when tossed, we first need to determine the total possible outcomes when two dice are rolled. Each die has 6 faces, which means:
Total outcomes = 6 (for the first die) × 6 (for the second die) = 36 outcomes.
Next, we look for the specific outcomes that meet our condition—in this case, both dice showing a one. The only outcome that satisfies this is (1, 1).
Therefore, there is only 1 favorable outcome (both dice showing a one).
To calculate the probability, we use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Substituting our numbers:
Probability = 1 / 36
Thus, the probability that both dice will show a one is 1/36. This means that if you were to roll two dice a large number of times, you would expect to see the pair (1, 1) approximately once every 36 rolls.