Final answer:
The keyword 'mutually exclusive' in probability refers to events that cannot occur simultaneously, with P A AND B = 0. An example of mutually exclusive events is flipping a coin and getting both heads and tails. Additionally, the complement in probability refers to all the outcomes not included in a specific event, and the sum of an event and its complement's probabilities is always 1.
Step-by-step explanation:
The keyword 'mutually exclusive' is associated with a probability concept where two events cannot occur at the same time. If events A and B are mutually exclusive, the probability of both events occurring together, denoted as PA AND B, is zero. For example, when flipping a coin, the events of landing on heads and tails are mutually exclusive because the coin cannot land on both sides simultaneously.
We can further explore this concept by examining a scenario involving two events, G and E. If G and E are mutually exclusive, it means PG AND E = 0. To justify whether two events are mutually exclusive, one often uses numerical probabilities. For instance, if P G = 0.5 and P E = 0.3, and the probability of their intersection PG AND E is calculated to be 0, then G and E are mutually exclusive.
Complementing this, the term 'complement' in probability refers to the event that includes all the outcomes that are not part of a specific event. If E is an event, the complement of E, denoted by Ec or E', consists of all outcomes that are not in E. The probabilities of an event and its complement always add up to 1, as they make up the entirety of the sample space.