where X = “you roll two 6s in a row by roll N”, Y = “you roll at least two 6s by roll N”, and Z = “the first N rolls are all even”.
This is valid, right? And not particularly relevant to the stated problem, due to the “by roll N” qualifiers mucking up the statements in complicated ways?
Here’s the reasoning I intuitively want to apply:
(X→Y)→P[Y|Z]≥P[X|Z]
where X = “you roll two 6s in a row by roll N”, Y = “you roll at least two 6s by roll N”, and Z = “the first N rolls are all even”.
This is valid, right? And not particularly relevant to the stated problem, due to the “by roll N” qualifiers mucking up the statements in complicated ways?