Oops, I changed it to a more unintuitive one right after you replied! In my original comment, I said "you flip two coins, and you only know that at least one of them landed on heads. What is the probability that both landed on heads?"

And... No! Conditional probability strikes again! When you flipped those coins, the four possible outcomes were TT, TH, HT, HH

When you found out that at least one coin landed on heads, all you did was rule out TT. Now the possibilities are HT, TH, and HH. There's actually only a 1/3 chance that both are heads! If I had specified that one particular coin landed on heads, then it would be 50%

[–] GhostsAreShitty@lemmy.world 3 points 11 months ago (3 children)

You’ve also ruled out TH by knowing one is heads. So the only possibilities are HT and HH. Is that not 50/50?

[–] starman2112@sh.itjust.works 3 points 11 months ago (1 children)

At least one is heads, but unless you know which one it is, you haven't ruled out HT or TH

[–] Glide@lemmy.ca 7 points 11 months ago* (last edited 11 months ago)

But you do know which one it is, because you said "other child". As soon as you ask the question, you assign a specific outcome to a specific child eliminating HH and HT (or in the new example, BB and BG). "What are the odds they have a female child" and "what are the odds the other child is female" are not the same question.

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