The second relevant statistical notion is Bayes’s theorem, a mathematical proposition that tells us how to update our estimates of people, events and situations in the light of new evidence.

A mathematical example: Three coins are before you. They look identical,
but one is weighted so it lands on heads just one-fourth of the time;
the second is a normal coin, so heads come up half the time; and the
third has heads on both sides.

Pick one of the coins at random. Since there are three coins, the
probability that you chose the two-headed one is one-third. Now flip
that coin three times. If it comes up heads all three times, you’ll very
likely want to change your estimate of the probability that you chose
the two-headed coin. Bayes’s theorem tells you how to calculate the new odds; in this case it says the probability that you chose the two-headed coin is now 87.7 percent, up from the initial 33.3 percent.

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