Probability notation

Question

I want to ask you about the notation in probability.

I know that

P(A | B) = the conditional probability that event A occurs given that event B has occurred already

But I cannot find what A,B or in my case P(A|B,C). I suggest it means "the conditional probability that event A occurs given that B and C BOTH occurred already"

I don't know what the comma means.

Can you help me ?

Solution 1

You are basically correct.

P(A| B) is the probability of A given B. P(A| B, C) is the probability of A given (B and C).

You could just as easily write it as P(A| B ∧ C) but it is notational convention to use a comma. Think of everything after the vertical bar as a list of the given things, separated by commas.

(And note that the vertical bar is a very high precedence operator, so to speak.)

Solution 2

This is according to Bayes rule

P(C|A,B) = P(A,B|C).P(C) / P(A,B)