Final answer:
Mutually exclusive events are occurrences in probability that cannot happen simultaneously. Their probabilities are added together to find the total probability of either event occurring. This concept is widely applicable in various probability and statistics scenarios.
Step-by-step explanation:
Mutually exclusive events in probability are those that cannot happen at the same time. For example, the probability that a washing machine will need repairs during a six-year period is 0.10; this event and the event that the machine will not need repairs are mutually exclusive since only one outcome can occur.
When calculating probabilities for mutually exclusive events, you simply add the probabilities of each event occurring separately. If, hypothetically, the probability of a machine not needing repairs were 0.90, the total probability would be 0.10 (repairs needed) + 0.90 (no repairs needed) = 1, since these are the only two possible outcomes.
The provided examples from different scenarios all pertain to calculating probabilities in various contexts, indicating that understanding and identifying mutually exclusive events is useful in various applications within probability and statistics.