Suppose I flip two coins, without letting you see the outcome, and I tell you that at least one of the coins came up heads, what is the probability that the other coin is also heads?
You might initially think that the answer is 1/2, however, it isn't.
Before I tell you anything, all you know is I've flipped two coins, and the possible outcomes are:
HH, HT, TH, TT
I now tell you that there was at least one head, which eliminates TT, leaving three possibilities. Of these three possibilities, only 1 allows the second head: HH. So the probability is 1/3. QED.
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