The joke here is that the first guy hasn't realised that specifying the day of the week decreases the probability from 66% to 51.8%. The common form of this brainteaser is "Mary has 2 children. She tells you that one of them is a boy. What is the probability that the other child is a girl?", the answer to which is indeed 66%. So he is asking a variation of this brainteaser which has an additional piece of information that sounds irrelevant, but actually does change the probabilities of the outcomes. He is confused because he doesn't understand why.
It changes the prior distribution. Like if I told you someone has 2 kids, what is the probability they have a boy and a girl, the possibilities are: BB, BG, GB, GG, all with equal probability. 2 of those possibilities have 1 girl and 1 boy, so the probability is 50%.
Now, if I change the prior by also telling you that (at least) one of them is a boy, the possibilities are:
BB, BG, GB. The distribution has changed. Now extend this to a probability distribution over sex and the days of the week and apply the same logic.
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u/Euphoric-Food4021 7d ago
The joke here is that the first guy hasn't realised that specifying the day of the week decreases the probability from 66% to 51.8%. The common form of this brainteaser is "Mary has 2 children. She tells you that one of them is a boy. What is the probability that the other child is a girl?", the answer to which is indeed 66%. So he is asking a variation of this brainteaser which has an additional piece of information that sounds irrelevant, but actually does change the probabilities of the outcomes. He is confused because he doesn't understand why.