Probability is hard.The difficulty is that too many people don't understand what it means to be independent in the sense of probability and why that is required for the arguments. They simply take Hoyle's word for it and go.
I still hate the Monty Hall paradox.
I know...I know....always switch.
And I see the basic reason why.
I still hate it.
And we all know that hate is the mind killer.
My hebitude is why I'm only an engineer.