Probability Theorem

Multiplication theorem on probabilities for independent events:

If two events A and B are independent, the probability that both of them occur is equal to the product of their individual probabilities. i.e P(AÇB) = P(A) . P(B)

The theorem can be extended to three or more independent events. If A,B,C……. be independent events, then P(AÇBÇC…….) = P(A).P(B).P(C)……

If A and B are independent then the complements of A and B are also independent. i.e P(A Ç B ) = P(A) . P(B)

Multiplication theorem for dependent events:

If A and B be two dependent events, i.e the occurrence of one event is affected by the occurrence of the other event, then the probability that both A and B will occur is

P(A Ç B) = P(A) P(B/A)

In the case of three events A, B, C, P(AÇBÇC) = P(A). P(B/A). P(C/AÇB). ie., the

probability of occurrence of A, B and C is equal to the probability of A times the probability of B given that A has occurred, times the probability of C given that both A and B have occurred.