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Question about solution

To this question: https://brilliant.org/practice/probability-is-everywhere/?p=3

I get that since we don't gain any information, the probability space stays the same. What I don't understand is that since we know how many chocolates were taken out why can't we use that information to calculate the probability?

Like this: Friend takes a chocolate. Chance that it was cherry over the chocolate is 1/2. We then know that the chance of it being a cherry the second time is 4/9. Multiply the two, and you get 4/18 -> 2/9.

I guess there's some flaw in my logic, but I can't for the life of me figure it out.

Note by Andrew Turner
2 weeks ago

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You can: there is a \(1/2\) chance that he took a cherry, in which case you have a \(4/9\) chance to eat a cherry. And there's a \(1/2\) chance that he took a chocolate, in which case you have a \(5/9\) chance to eat a cherry. So the answer is still \(1/2 \cdot 4/9 + 1/2 \cdot 5/9 = 1/2.\)

Patrick Corn - 1 week, 6 days ago

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what is the purpose of adding both cases together?

Andrew Turner - 1 week, 6 days ago

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