Final answer:
The probability that at least one six-sided die shows a 3 when rolling two dice is 11/36, calculated using the complement rule (1 - probability of the event not occurring).
Step-by-step explanation:
The question you've asked involves calculating the probability that at least one die shows a 3 when you roll two fair six-sided dice. To find this probability, we can use the complement rule which says that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
The probability that a single die does not show a 3 is 5/6 because there are five other outcomes on the die (1, 2, 4, 5, 6). Since the dice are independent, the probability that neither die shows a 3 when you roll both at the same time is (5/6) × (5/6), which is 25/36.
Therefore, the probability that at least one die shows a 3 is the complement of this, calculated as 1 - (25/36), which simplifies to 11/36. So, there is an 11/36 chance that at least one die will show a 3.