12 terms

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)