What are mutually exclusive events?

Mutually exclusive events are defined as events that cannot occur simultaneously. This means that if one event happens, the other cannot happen at the same time. For example, when flipping a coin, the outcomes of getting heads or tails are mutually exclusive; if the coin lands on heads, it cannot also land on tails during the same flip. This concept is important in probability because it affects how probabilities are calculated for combined events. When dealing with mutually exclusive events, the probability of either event occurring is simply the sum of their individual probabilities. Thus, the understanding of mutually exclusive events is foundational in probability theory and helps to clarify the interactions between different possible outcomes in statistical analyses.