I’m not a statistician, but I think that this dilemma might simply sound like other, much trickier probability issues.
One of the misleading aspects of it is this line: ‘When asked what the probability is that the coin came down tails, you of course answer “.5”.’ The problem is that this is posed in the past tense, but (without any other information whatsoever) the subject must treat it the same way as the question about a future situation: ‘What is the probability that a fair-coin would come down tails, all other things being equal?’
But the next time the question is asked, there’s a result to tie it to. It is an actual event with observable secondary effects, and you can hazard an educated guess based on the new information at hand.
Perhaps your thought-experiment vaguely references the counter-intuitive notion that if a coin is flipped 99 times and comes up tails every time, the chances of it coming up tails again is still just .5. But it’s more like if you had a jar or 100 marbles, containg either 99-white/1-black or 1-white/99-black and you reached in without looking. What is the probability that you managed to pick that 1 out of 100? It’s the same principle that is at work in the Monty Hall problem.
I’m not a statistician, but I think that this dilemma might simply sound like other, much trickier probability issues.
One of the misleading aspects of it is this line: ‘When asked what the probability is that the coin came down tails, you of course answer “.5”.’ The problem is that this is posed in the past tense, but (without any other information whatsoever) the subject must treat it the same way as the question about a future situation: ‘What is the probability that a fair-coin would come down tails, all other things being equal?’
But the next time the question is asked, there’s a result to tie it to. It is an actual event with observable secondary effects, and you can hazard an educated guess based on the new information at hand.
Perhaps your thought-experiment vaguely references the counter-intuitive notion that if a coin is flipped 99 times and comes up tails every time, the chances of it coming up tails again is still just .5. But it’s more like if you had a jar or 100 marbles, containg either 99-white/1-black or 1-white/99-black and you reached in without looking. What is the probability that you managed to pick that 1 out of 100? It’s the same principle that is at work in the Monty Hall problem.