- #26

mfb

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At least one of the pens was black. What is the probability the other one was blue?

You can use the standard answer of 2/3 - and be wrong.

Why? Before I drew the pens, I decided to post this puzzle only if the colors are matching. There was never a chance of mismatching colors for this puzzle.

The frequentist approach does not work here as the children are either boys or girls (each) - there is no actual probability involved. It is possible to take the Bayesian approach - but then we also have to ask "given the different girl/boy combinations, how likely is it to get the information 'at least one is a boy born on Tuesday'?". And there is no meaningful way to assign a specific probability to that.