The events (A_{1}, A_{2}, ldots, A_{n}) are independent; (Pleft(A_{k} ight)=p_{k}). Find the probability of: (a) the occurrence

The events \(A_{1}, A_{2}, \ldots, A_{n}\) are independent; \(P\left(A_{k}\right)=p_{k}\). Find the probability of:

(a) the occurrence of at least one of these events;

(b) the nonoccurrence of all these events;

(c) the occurrence of exactly one event (it is immaterial which).