Dear allstatters,
I have a question on probabilities.
Let’s say we have three events A, B and C where C is a subset of B and B is a
subset of A. This implies that C is a subset of A.
When it comes to consider probabilities we can calculate
P(B|C)
P(A|B,C)
Can we calculate P(A|B)? Does this exist and is this different from P(A|B,C)?
What it seems to me is that “A|B” actually implies conditioning on C, thus “A|B
and C” is actually correct, and “A|B” is simply a not complete notation. So,
writing P(A|B) is actually identical to P(A|B,C) a part from the clarity of
conditions.
Con anyone confirm or correct these statements?
Thanks a lot in advance for any answer.
Nico
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