In the probability course, under multiplication rule chapter, author said that
P(A intersection B) = P(A|B) * P(B).
But, in next chapter (Bayes rule), he says
P( A intersection B) = P(B|A)*P(A).
Why the change? Can we use them interchangeably?
I don’t know if I am missing something, but I appreciate any assistance.
The two are equivalent since AnB = BnA.
P(A|B) * P(B) = P(A intersection B) = P(B intersection A) = P(B|A) * P(A)
Hence, we can use them interchangeably.