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Watch out. Because your bits are indexed you have a different problem than before. The first red ball does not give you a significant bit.

Instead: Make a sample and now you know that it is greater than a random number unknown to you. Can you derive any knowledge about your next sample?

Indeed, indexing changing probabilities is very unintuitive for most people. Here's another fun one.

There's two coins on the table that you don't see. The only information provided is that

a) one of them is tails b) the left one is tails

What is the probability of both being tails?

It's 1/3 in (a) and 1/2 in (b). The reasoning being:

1. At first both HH, HT, TH and TT are all equaly likely. 2. In case (a) we discard HH as an option, but in case (b) we discard *both* HH and HT.

Yes, my fault. In fact random numbers between 0 and 255 don't have the property that number-of-set-bits have uniform distribution.