I’m a bit surprised that you think this way, considering that you’ve basically solved the problem yourself in this comment.
P(Heads & Monday) = P(Tails & Monday) = 1⁄2
P(Tails & Monday) = P(Tails&Tuesday) = 1⁄2
Because Tails&Monday and Tails&Tuesday are the exact same event.
The mistake that everyone seem to be making is thinking that Monday/Tuesday mean “This awakening is happening during Monday/Tuesday”. But such events are ill-defined in the Sleeping Beauty setting. On Tails both Monday and Tuesday awakenings are supposed to happen in the same iteration of probability experiment and the Beauty is fully aware of that, so she can’t treat them as individual mutual exclusive outcomes.
You can only lawfully talk about “In this iteration of probability experiment Monday/Tuesday awakening happens”.
I’m a bit surprised that you think this way, considering that you’ve basically solved the problem yourself in this comment.
P(Heads & Monday) = P(Tails & Monday) = 1⁄2
P(Tails & Monday) = P(Tails&Tuesday) = 1⁄2
Because Tails&Monday and Tails&Tuesday are the exact same event.
The mistake that everyone seem to be making is thinking that Monday/Tuesday mean “This awakening is happening during Monday/Tuesday”. But such events are ill-defined in the Sleeping Beauty setting. On Tails both Monday and Tuesday awakenings are supposed to happen in the same iteration of probability experiment and the Beauty is fully aware of that, so she can’t treat them as individual mutual exclusive outcomes.
You can only lawfully talk about “In this iteration of probability experiment Monday/Tuesday awakening happens”.
In this post I explain it in more details.