It’s one of those phrases I just kinda nod my head and go “yeah” when I hear it. I’ve looked it up before, but the definition never stuck. Same thing happened with “survivorship bias,” but I eventually figured that one out.
I guess I need it explained in a different way for it to stick.
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Two things that cannot be true at the same time. You can only have one or the other but not both. They’re mutually exclusive, mutual in this case denoting a pair that are bound by something in common, which is exclusivity. Basically two things that are exclusive, so you can only have one of the two. The mutual part is the fact that it’s these two particular things that negate one another and not something else.
Two events are mutually exclusive if they can’t happen at the same time.
For example, if you flip a coin it can’t land heads AND tails on the same flip.
Or if you roll a die, it can’t land on 1 AND 6 on the same roll.
If A and B are mutually exclusive, then it means that A might happen or B might happen, but it is not possible for A and B to both happen.
Mutually exclusive means that things can’t be in both states of being at one time
Like you can’t have an apple and eat it and still have your apple it’s either not eaten or eaten.
Raw and cooked is another example, you can’t uncook something when it’s cooked and it’s no longer raw when you cook it so something can’t be both.
The simplest one is a on/off switch, a light can be on or off, even if the bulb is dim from low power it’s still “on”
But there can still be a transitional state in between these states it’s just that that particular states are exclusive to each other, so like the apple is being eaten is a transitional state
> Same thing happened with “survivorship bias,” but I eventually figured that one out.
For everyone else: Survivor bias is when (for instance) all the old buildings you see are pretty, because the ugly old buildings got knocked down. The set of *things that you see* is a biased sample of *things that ever were*, because some things got eliminated and others survived.
You’ve gotten good answers already, but I’ll focus on the words.
If you’ve got two possibilities, and the first possibility *excludes* the second possibility, that makes that possibility “exclusive”.
Likewise, if the second possibility *also* excludes the first possibility, it is also “exclusive”.
When both possibilities exclude the other, they are exclusive to each other, or mutually. Mutually exclusive.
Sometimes it’s not always clear how the words came to be used this way, in particular, “exclusive” is typically used in a way that means something more like “rare” or “desirable”, when what it means is “something that excludes”. An “exclusive club” is one that is tough to get into, it excludes people.
The point is, understanding how the word “exclusive” is actually used in this phrase might help you remember what it means.
Another way to see it is that mutually exclusive things DON’T OVERLAP with one another.
In analysis, the term MECE (Mutually Exclusive, Collectively Exhaustive) is often used.
It means the ideas to solution a problem have to be DISTINCT and NOT INTERFERE with one another, while all collectively covering all facets of the problem.
A good example of survivorship bias that I read somewhere, probably apocryphal:
During WW2, a lot of the fighter planes that were returning had tons of bullet holes around the wings and propellers. Some big shot general looked at them and said that we need to reinforce those areas because that’s where our boys are getting shot the most.
His engineers told him actually, that’s the exact OPPOSITE of what we need to do. The fact that those planes got shot there and still made it home safely means their armor is fine in those areas. On top of which, the planes that didn’t come back would’ve probably been shot on other areas like the fuselage or cockpit. So we need to reinforce THOSE areas.
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