In 1000 replications of the experiment, there will be an average of 1500 awakenings − 1000 on Monday, and 500 on Tuesday.
“Suppose this experiment were repeated 1,000 times. We would expect to get 500 heads and 500 tails. So Beauty would be awoken 500 times after heads on Monday, 500 times after tails on Monday, and 500 times after tails on Tuesday.”
Complete replications of the entire experiment is not the right approach, because the outcome of interest occurs at a single awakening. We need 1000 replications of the process that lead to an awakening.
“The process that lead to an awakening” refers not to one physical process, but potentially to multiple partly-overlapping physical processes per actual physical experiment.
You mean to run the physical experiment around 666 times, resulting in 1000 awakeningns in total—around 667 on Monday, and around 333 on Tuesday? Rather obviously that doesn’t support your maths either.
I have yet to find a sum that gives 500:250:250 as originally claimed. There is no 250 involved. Your supplied “probability tree” image is just nonsense—a wrong analysis of the problem, irrespective of what bet you think the question corresponds to.
I make it: 500 heads & Monday … 500 tails & Monday … 500 tails & Tuesday.
You are arguing with http://en.wikipedia.org/wiki/Sleeping_Beauty_problem about the problem—and are making math errors in the process.
Interesting. You want to replicate an awakening 1000 times, and you end up with 1500 awakenings. I’d be concerned about that if I were you.
In 1000 replications of the experiment, there will be an average of 1500 awakenings − 1000 on Monday, and 500 on Tuesday.
“Suppose this experiment were repeated 1,000 times. We would expect to get 500 heads and 500 tails. So Beauty would be awoken 500 times after heads on Monday, 500 times after tails on Monday, and 500 times after tails on Tuesday.”
http://en.wikipedia.org/wiki/Sleeping_Beauty_problem
What is it about this that you are not getting?
Complete replications of the entire experiment is not the right approach, because the outcome of interest occurs at a single awakening. We need 1000 replications of the process that lead to an awakening.
What you said further up this branch of the thread was:
“if you want to think about doing 1000 replications of the experiment, it should go like this”.
Now you seem to be trying to shift the context retrospectively—now that you have found out that all the answers you gave to this were wrong.
You know that’s not true. I didn’t just discover the ’500 500 500′ answer—I quoted it from wikipedia and showed why it was wrong.
I should have made it clear what I meant by experiment, but you know what I meant now, so why take it as an opportunity to insult?
I don’t know what you mean by “experiment”.
“The process that lead to an awakening” refers not to one physical process, but potentially to multiple partly-overlapping physical processes per actual physical experiment.
You mean to run the physical experiment around 666 times, resulting in 1000 awakeningns in total—around 667 on Monday, and around 333 on Tuesday? Rather obviously that doesn’t support your maths either.
I have yet to find a sum that gives 500:250:250 as originally claimed. There is no 250 involved. Your supplied “probability tree” image is just nonsense—a wrong analysis of the problem, irrespective of what bet you think the question corresponds to.
I don’t think it is accurate to describe my post as “insulting”.