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thomblake comments on Conditioning on Observers - Less Wrong
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Well, consider:
Scenario 1: You have a bag containing one red ball and an arbitrarily large number of green balls. You reach in and pull out one ball at random. What is the probability that the ball is red?
Scenario 2: You have a bag containing one red ball and another bag containing an arbitrarily large number of green balls. A fair coin is flipped; if heads, you are handed the bag with the red ball, and if tails you are handed the bag with the green balls (you can't tell the difference between the bags). You reach in and pull out one ball at random. What is the probability that the ball is red?
In scenario 1, P(red) is vanishingly small. In scenario 2, P(red) is 1/2.
The disanalogy is that you actually pull out all of the green balls, not just one.
Indeed - introducing amnesia and pulling out each of the green balls in turn might muddy this one up as well.