Random doesn’t necessarily mean uniform. When Beauty wakes up, she knows she is somewhere on the tails path with probability .5, and somewhere on the tails path with probability .5. If tails, she also knows it’s either monday or tuesday, and from her persepctive, she should treat those days as equally likely (since she has no way of distinguishing). Thus, the distribution from which we would select an awakening at random has probabilities 0.5, 0.25 and 0.25.
No, because my probability tree was meant to reflect how beauty should view the probabilities at the time of an awakening. From that perspective, your tree would be incorrect (as two awakenings cannot happen at one time)
After the 1000 experiments, you divided 500 by 2 - getting 250. You should have multiplied 500 by 2 - getting 1000 tails observations in total. It seems like a simple-enough math mistake.
No, that’s not what I did. I’ll assume that you are smart enough to understand what I did, and I just did a poor job of explaining it. So I don’t know if it’s worth trying again. But basically, my probability tree was meant to reflect how Beauty should view the state of the world on an awakening. It was not meant to reflect how data would be generated if we saw the experiment through to the end. I thought it would be useful. But you can scrap that whole thing and my other arguments hold.
Well you did divide 500 by 2 - getting 250. And you should have multiplied the 500 tails events by 2 (the number of interviews that were conducted after each “tails” event) - getting 1000 “tails” interviews in total. 250 has nothing to do with this problem.
Random doesn’t necessarily mean uniform. When Beauty wakes up, she knows she is somewhere on the tails path with probability .5, and somewhere on the tails path with probability .5. If tails, she also knows it’s either monday or tuesday, and from her persepctive, she should treat those days as equally likely (since she has no way of distinguishing). Thus, the distribution from which we would select an awakening at random has probabilities 0.5, 0.25 and 0.25.
This appears to be where you are getting confused. Your probability tree in your post was incorrect. It should look like this:
If you think about writing a program to simulate the experiment this should be obvious.
No, because my probability tree was meant to reflect how beauty should view the probabilities at the time of an awakening. From that perspective, your tree would be incorrect (as two awakenings cannot happen at one time)
After the 1000 experiments, you divided 500 by 2 - getting 250. You should have multiplied 500 by 2 - getting 1000 tails observations in total. It seems like a simple-enough math mistake.
No, that’s not what I did. I’ll assume that you are smart enough to understand what I did, and I just did a poor job of explaining it. So I don’t know if it’s worth trying again. But basically, my probability tree was meant to reflect how Beauty should view the state of the world on an awakening. It was not meant to reflect how data would be generated if we saw the experiment through to the end. I thought it would be useful. But you can scrap that whole thing and my other arguments hold.
Well you did divide 500 by 2 - getting 250. And you should have multiplied the 500 tails events by 2 (the number of interviews that were conducted after each “tails” event) - getting 1000 “tails” interviews in total. 250 has nothing to do with this problem.