The Grammarphobia Blog

Mutually exclusive interests

Q: In common usage, “mutually exclusive” refers to things that are totally separate. But in statistics, it refers to characteristics that all converge. Example: 1) over six feet tall, 2) brown eyes, and 3) blond hair. Your thoughts?

A: “Mutually exclusive” has two garden-variety definitions in standard dictionaries.

It can mean simply incompatible (as in “their interests were mutually exclusive”). Or it can mean related in such a way that one excludes or precludes the other (as in “mutually exclusive choices”). 

But “mutually exclusive” also has specialized meanings in logic as well as in probability and statistics.

In logic, two mutually exclusive propositions cannot both be true.

In probability and statistics, two mutually exclusive events (also called “disjoint events”) can’t happen at the same time. The occurrence of one means the other cannot occur, so the probability that both will happen is zero.

In addition, statistical categories are said to be mutually exclusive if an individual or object can be included in only one of them.

In the example you give, the three categories (over six feet tall, brown eyes, blond hair) are not mutually exclusive, since a single individual could theoretically be counted in all three.

Mutually exclusive categories would be, for example, over six feet tall and under six feet tall, or male and female. One individual can’t be counted in both. 

Here’s a citation from the Oxford English Dictionary that illustrates the technical use of “mutually exclusive.” It comes from Douglas Chalmers Hague’s book Managerial Economics (1969):

“To be drawn up correctly, our list of probabilities must be such that if any one event occurs, this automatically rules out the possibility that any other event in the same list could also occur. The events will then be mutually exclusive.”

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