Final answer:
To determine if the events of going to college, working full-time, or taking a gap year are mutually exclusive, definitions or conditions need to be clear. If students can only choose one path without overlap, then the events are mutually exclusive. However, without additional information, we cannot conclusively state whether these events are mutually exclusive.
Step-by-step explanation:
The question concerns whether certain events in a scenario involving a high school graduating class are mutually exclusive. Mutually exclusive events are those that cannot occur at the same time—the occurrence of one event precludes the occurrence of another. For example, a single student cannot both be going to college and taking a gap year simultaneously if these options are defined as mutually exclusive.
In the given scenario, the high school graduating class consists of 300 students with 200 planning to go to college, 40 planning to work full-time, and 80 taking a gap year. To determine if these events are mutually exclusive, one would have to understand if a student could belong to more than one of these groups at the same time. If a student can only choose one of these paths, and the groups do not overlap, then they would indeed be mutually exclusive. Conversely, if a student could, for instance, go to college and simultaneously work full-time, then the events would not be mutually exclusive.
There is not enough information given to make a conclusive statement about the exclusivity of these events. It is necessary to know more about the definitions or conditions set by the high school or the students' intentions. Under typical assumptions and traditional definitions, these events might be considered mutually exclusive as they represent distinct post-graduation plans; however, without specific details, one cannot say for certain.