I don't think this is correct. It matters whether the person removing the second ball can see the colors and choose accordingly. If you can, and you willingly remove a single blue ball, you have the Monty hall problem where you stick to your choice. It does not influence the chances, it is still 1/2. But the way I read the problem, you choose a ball at random, look at its color, it happens to be blue. Now this gives you information on the composition of the remaining balls. The chance is 1/3.
To drive home the point that removing a ball "can influence" the odds of the first ball: what if you took out an extra ball that turns out to be blue? You now have two blue balls, leaving the chance the first ball was blue zero.
The sneaky part of this question is that it gives information about the outcome and then asks you again about the probability. Forget the extra balls, and just drive the point home directly: suppose I pick a ball at random, and show it to you. It’s blue. I ask: “what are the odds that the ball is blue?” (exact phrasing as original question).
There are obviously correct interpretations for 50% and 100%. It depends whether I’m asking:
- What’s the probability of this outcome?
- What’s the probability that the ball I’m holding in my hand in blue?
The second is effectively a “resampling” with a population of one. You are simply assuming the second interpretation and arguing for it, but I don’t dispute the logic. The original question is unclear whether it’s asking for the probability that you picked a blue ball initially (50%) or the likelihood that the ball is blue, given some information of the outcome. But we don’t normally speak of probabilities this way. The odds that you picked a blue ball initially were 50%, even if you picked a red one.
By giving only partial information, the question creates more ambiguity since the answer isn’t definite. (When there is ambiguity in a question, I believe most people will discard trivial interpretations over substantive ones, which is what pushes toward the “resample” here.)
Anyway, I’ll leave it there since I think it’s clear there are correct interpretations for both, depending on what the question is actually asking.
