Statement: Let A and B be any two independent events with respective probabilities P(A) and P(B). Then, the probability of occurrence of events A and B is P(A∩B) = P(A). P(B)
Proof: Suppose, a random experiment, results ‘n’ outcomes, of which’m’, outcomes are favorable k to events A and another random experiment results n2 outcomes of which m2 outcomes are favorable to event B.
The occurrence of the events A and B together m1 and m2 i.e., m1 × m2 favorable events out of n1, and n2 i.e., n1 × n2 outcomes.
∴ Probability of ocurrence of events A and Btogther is.
Hence the proof.