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7/17/2019 Midterm CheatSheet
http://slidepdf.com/reader/full/midterm-cheatsheet-568d4a3a19074 1/1
1 Conditional Probability
• Bayes’ Rule
P (A ∩B) = P (B)P (A|B) = P (A)P (B|A)
• Bayes’ Rule Odd form:
Odd(A|B) = P (A|B)
P (Ac|B) =
P (B|A)
P (B|Ac)
P (A)
P (Ac)
• Conditional probability satisfies all the properties of probability.
P (A|B, E ) = P (B|A,E )P (A|E )
P (B|E )
P (B|E ) =
n
i=1
P (B|Ai, E )P (Ai|E )
• Disjoint vs Independence
P (A ∩B) = 0 (Disjoint)
P (A ∩B) = P (A)P (B) (Independent)
• If A and B are independent, then A and Bc, Ac and B, Ac and Bc arealso independent.
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