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Bayes rule

Bayes rule

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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.

Thank you.

1 Answer

365 Team

Hey Abhiram, 
 
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. 
 
Best, 
365 Vik

Thank you.

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