What occurs when you add the probabilities of mutually exclusive events?

When dealing with mutually exclusive events, it is essential to understand how their probabilities interact. Mutually exclusive events are those that cannot happen at the same time; for instance, when rolling a die, the events of rolling a 1 or rolling a 2 cannot occur simultaneously.

The sum of the probabilities of these events is particularly important. When the mutually exclusive events exhaust all possible outcomes, their individual probabilities can be added together to yield a total probability of 1. This means that if the outcomes cover all scenarios without overlap, the combined likelihood of one of these outcomes occurring reaches a certainty (1).

For example, if you have event A with a probability of 0.3 and event B with a probability of 0.4, and together they account for all outcomes, then adding their probabilities would yield 0.3 + 0.4 = 0.7. However, if events A and B encompass all potential outcomes (including all other possible outcomes together adding up to 0.3 + 0.4 + 0.3 = 1), this satisfies the condition of mutual exclusivity and covering all possibilities.

Thus, when mutually exclusive events are defined in a complete probability space, their summed probabilities will equal 1