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(BA) by using the knowledge of P(B), P(AB) 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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 Spring '14
 Conditional Probability, Probability, Probability theory

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