1.

Define : Multiplication Theorem on Probability.

Answer»

Statement I. If two events A and B are independent, then probability that they will both occur is equal to the product of their individual probabilities. 

i.e. P (A and B) = P (A) × P (B)               [‘AND’ rule] 

In set notation, P (A ∩ B) = P (A) × P (B) 

Note. If A, B, C are independent events, then 

P (A and B and C) =P (A) × P (B) × P (C) 

In set notation, P (A ∩ B ∩ C) = P (A) . P (B) . P (C). 

In general, if A1, A2, ..... An are n independent events, then 

P (A1 and A2 and A3 and ..... An) = P(A1) × P(A2) × P(A3) × ..... × P(An

In set notation, P(A1 ∩ A2 ∩ A3 ..... ∩ An) = P(A1) × P (A2) ..... × P (An

Finding probabilities of simultaneous occurrence of two independent events. 

Method. Use the relation P (A ∩ B) = P (A) . P (B).



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