- #1
TheKracken
- 356
- 7
Homework Statement
and is in reference to the intersection of a set.
I know the formula that P(A and B ) = P(B) * P(A|B)
Now we are given something of the nature of P(A and B and C) I am trying to figure out a formula for this. From my searches on google I only find people giving the formula and I really would like to figure it out for my self.
Here is my attempt even though it does not appear to align with the correct formula.
P(A and B and C) = P((A and B) and (C)
= P(K and C ) ; such that P(A and B) = P(K)
= P(C) * P(K|C) ( now I need to do ( B|A)
= P(C) *P(A and B|C)*P(B|A)
What exactly am I doing wrong? I must have made some sort of logical error.
Correct answer should be
P(A)*P(C|A and B) *P(B|A)