Final answer:
Neither Event A nor Event B has exactly 12 outcomes when tossing two 12-sided dice; Event A has 36 outcomes and Event B has 16 outcomes. The student has asked to identify an event that has exactly 12 outcomes in the context of tossing two 12-sided dice, where each die shows numbers from 1 to 12.
Step-by-step explanation:
The student has asked to identify an event that has exactly 12 outcomes in the context of tossing two 12-sided dice, where each die shows numbers from 1 to 12. Let's first analyze Event A, which is the event where both dice show an even number. Since there are six even numbers on each die (2, 4, 6, 8, 10 and 12), there are 6 outcomes possible for one die. However, since there are two dice, we need to multiply the number of outcomes of the first die by the number of outcomes of the second die (6 * 6), which equals 36 total outcomes for Event A, not 12 outcomes.
Now, let's examine Event B, where both dice show a number greater than eight. The numbers greater than eight on one die are 9, 10, 11, and 12, which yields 4 outcomes for one die. Similar to Event A, we multiply these outcomes for one die for the first die by the outcomes for the second die (4 * 4) to get the total number of outcomes. This results in 16 total outcomes for Event B, not 12. Therefore, neither Event A nor Event B has exactly 12 outcomes. To find an event with exactly 12 outcomes, we would need to consider different conditions or events that can occur with two 12-sided dice.
In math, an outcome is a result of an event that depends on probability, and any event can have more than one possible outcome. A simple event involves only one event and has only one outcome per event, while a compound event involves two or more events and can have a combination of two or more outcomes per event.