Explanation of Mutually Exclusive and Exhaustive Events
Mutually exclusive events are events that cannot occur at the same time. This means that if one event happens, the other event cannot happen simultaneously. On the other hand, exhaustive events are events that cover all possible outcomes of an experiment. This means that at least one of the events in the set will occur.

Events A, B, and C
In this scenario, events A, B, and C are mutually exclusive and exhaustive. This means that only one of the events can occur, and at least one of the events will occur. If event A occurs, then events B and C cannot occur. The same applies to events B and C.

p(A) + p(B) + p(C) = 1
Since events A, B, and C are exhaustive, the sum of their probabilities must equal 1. This is because one of the events must occur. If the sum of the probabilities is less than 1, then there are missing outcomes. If the sum is greater than 1, then there are overlapping outcomes. Therefore, the probabilities of events A, B, and C must add up to 1.
In conclusion, events A, B, and C are mutually exclusive and exhaustive. This means that only one of the events can occur, and the sum of their probabilities must equal 1.