Warning: this is a technical post. It’s really to see if I can clarify ideas in my mind by setting it to paper …. errr …. screen. And it’ll give you a peek into Statistics 421.

In probability theory, mutual exclusivity and independence are important concepts that often are misunderstood and wrongly viewed as one and the same. The fact is, they are essentially opposite. These concepts (particularly independence) are very important in providing a basic foundation to statistical theory.

Say there are two events, A and B. These events are mutually exclusive if by one’s occurence the other is precluded from occuring. If A = “event that I shaved this morning” and B = “event that I did not shave this morning,” the events are mutually exclusive. By virtue of A happening, B CAN’T happen.

Two events, A and B, are independent if one’s occurance has no effect on the occurance of the other. Say A = “event John Kerry becomes president” and B = “event that my head itches.” A has no connection with B. However, if we defined B = “event that all independents voted for John Kerry,” you can see that A and B could influence each other.

When you think of the two concepts without really thinking them through, you think that events that are mutually exclusive would also be independent, when actually, events HAVE to be dependent on one another if they are mutually exclusive.

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