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.