Conditional Probability and Independence

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P(E|F)
(P(E intersection F))/P(F)
independence
P(E|F) = P(E) so P(E intersection F) = P(E)P(F)
What is a partition of a sample space?
A collection of disjoint events E1, E2, ..., En in the sample space such that E1 U E2 U ... U En = the sample space.
What is E independent of F equivalent to?
F is independent of E
Theorem of total probability
Let E1, E2, ..., En be a partition of the sample space and let F be a subset of the sample space. Then P(F) = the sum up to n of P(F|Ei)P(Ei).
What is it important to remember to before answering a probability question?
Set up suitable notation for events.
Bayes' theorem simple form
P(E|F) = P(F|E)P(E)/P(F)
Bayes' theorem general form
P(Ei|F) = P(F|Ei)P(Ei)/(sum up to b of P(F|Ei)P(Ei)
E, F and G are mutually independent
P(E intersection F intersection G) = P(E)P(F)P(G)
P(A|B intersection F)
P(A intersection B | F)/P(B|F)
If A and B are independent what is P(A|B intersection C) equal to?
P(A|C)
If A and B are independent what is P(A intersection B|G)
P(A|G)P(B|G)
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