Introduction of Conditional Probability

If E and F are two events associated with the same sample space of a random experiment, the conditional probability of the event E given that F has occurred, i.e. P (E|F) is given by
P(E|F) = Number of elementary events favourableto E ∩ F/Number of elementary events which are favourable to F
P(E|F) = P(E ∩ F)/P(F) or
P(F|E) = P(E ∩ F)/P(E)

Properties of Conditional Probability

1. If E and F be events of a sample space S of an experiment, then we have P(S|F) = P(F|F) = 1 2. If A and B are any two events of a sample space S and F is an event of S such that P(F) ≠ 0, then we have P((A ∪ B)|F) = P(A|F) + P(B|F) – P((A ∩ B)|F) 3. P(E′|F) = 1 − P(E|F)

Multiplication Theorem on Probability


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