Final answer:
The question addresses the concepts of mutually exclusive and independent events in mathematics, specifically probability. Mutually exclusive events cannot occur simultaneously, while independent events do not affect each other's outcomes.
Step-by-step explanation:
The subject of this question is the concept of mutually exclusive and independent events within probability, which falls under the umbrella of mathematics. We use these terms to describe the relationship between two events, typically represented by the probability that they will occur together or in relation to one another.
Two events are mutually exclusive if they cannot occur at the same time. This is represented mathematically by the fact that the probability of both events occurring together (P(A AND B)) is 0. An example of mutually exclusive events is drawing a card from a deck and having it be both a red card and a black card at the same time, which cannot happen.
Events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. This is mathematically represented by P(A AND B) being equal to P(A) multiplied by P(B). If this equality holds true, then events A and B are independent; if not, they are dependent on each other. An example of independent events might be flipping a coin and rolling a die; the outcome of the coin flip does not affect the outcome of the die roll.