b is called the conditioning event idea of bayes

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Unformatted text preview: is called the conditioning event. Idea of Bayes Theorem: Sometimes we know the conditional probabilities in one direction but we are interested to find out the conditional probability in another direction. Bayes theorem gives us a way to compute P(B|A) by using the knowledge of P(B), P(A|B) and P(A| Rules of probability: I have collected some of rules you find useful in solving problems. For any event A, 0≤ P(A) ≤ 1 For sample space S, P(S) is always 1 P( ) = 1 – P(A) For two events A and B, P(A\B) = P(A) , P(B\A) = P(B) – P( So, P(A\B) is NOT same as P(B\A) For disjoint events , , ,…, , probability of their union P( …… ) = P( This is called the addition rule of probability. Warning: Do not use this result if they are not disjoint. For any two events A and B P( A For any three events A, B and C P( A For any two events A and B, we can always write: B = (B ) Hence, we can apply the addition rule to write: P(B) = P(B ) + P( ) (Think about why we can use the addition rule in this ca...
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