If A1, A2, ... , Ag are exhaustive and mutually exclusive events associated with a random experiment such that P(A; occurs) = pP;, where p, + P2 + ... if the experiment is repeated n times, then the...

Prove the theorem

Extracted text: If A1, A2, ... , Ag are exhaustive and mutually exclusive events associated with a random experiment such that P(A; occurs) = pP;, where p, + P2 + ... if the experiment is repeated n times, then the probability that A, occurs r¡ times, A2 occurs r, times, + Pk = 1, and %3| 1 Ar occurs r, times is given by •.•) n! rk Pk r2 Pi P„(r], r2> r): r!r!..! ... •.. where rị + r2 + ... + ry = n.