16.8: Coincidence

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Some things strike us a very unusual and unlikely. This often leads us to think that there “must be something special going on” when they do occur— surely, they couldn’t “just happen by chance.” Wilbur survives a disease that is fatal to 99.8% of the people who contract it, so something special must be going on. In fact, though, there will be two people out of every thousand who do survive. When Wilbur’s doctor first saw the test results, he thought it very unlikely that Wilbur would make it, and when Wilbur does the doctor is amazed. But there must be two people who are the lucky pair in a thousand, and it may just have happened to be Wilbur.

As we saw earlier, if we describe an event in enough detail, it will seem very unlikely (before the fact) that it will occur. Suppose you toss a quarter ten times. The probability of any sequence of outcomes is (1/2)₁₀which means that each possible set of outcomes is extremely unlikely. But when you do the tossing, one of these very unlikely sequences will be the one that you get.

There are countless examples of this. Before you tee off, the probability of the ball landing in any spot is close to zero. But if you hit it, it will land some place or another, even though it was very unlikely that it would alight precisely where it eventually does. So, things that seem unlikely can, and do, happen just by chance. Indeed, if we describe things in enough detail, almost everything that happens would have seemed unlikely before it occurred. Still, one of these unlikely things will occur.