Good formulation. “Given it’s Monday” can have two different meanings:
you learn that you will only be awoken on Monday, then it’s 50%
you awake assign 1⁄3 probability to each instance and then make the update P(T|M)=P(M|T)P(T)/P(M)=(1/2)(2/3)/(2/3)=50%
So it turns out to 50 % for both but it wasn’t initially obvious to me that these two ways would have the same result.
Good formulation. “Given it’s Monday” can have two different meanings:
you learn that you will only be awoken on Monday, then it’s 50%
you awake assign 1⁄3 probability to each instance and then make the update P(T|M)=P(M|T)P(T)/P(M)=(1/2)(2/3)/(2/3)=50%
So it turns out to 50 % for both but it wasn’t initially obvious to me that these two ways would have the same result.