Final answer:
To find the probability of at least one die showing a 3 when rolling two fair six-sided dice, calculate the probability of the complementary event. There is a 86.11% chance of at least one die showing a 3.
Step-by-step explanation:
To find the probability that at least one die shows a 3 when rolling two fair six-sided dice, we can calculate the probability of the complementary event, which is the probability that no die shows a 3. Let's break it down:
There are 6 possible outcomes for each die roll, so the total number of outcomes for rolling two dice is 6 x 6 = 36.
Out of these 36 outcomes, there are 5 outcomes where both dice show a 3 (3,3), so the probability of both dice showing a 3 is 5/36.
Therefore, the probability of at least one die showing a 3 is 1 - (5/36) = 31/36, which is approximately 0.8611 or 86.11%.