Show that two independent events with positive probabilities can't be mutually exclusive and vice versa.

Give the definition of mutually exclusive events.

Define with examples : Mutually exclusive events.

Can two mutually exclusive events with positive probabilities be independent ? Give reasons.

If the events A and B are mutually exclusive then-

State and prove the " addition theorem" of probability for two mutually exclusive events.

Let A and B be two independent events. The probability of their simultaneous occurrence is 1/8 and the probability that neither occurs is 3/8. Find P(A)a n dP(B)dot

If A and B are two mutually exclusive events, then-

If A and B are two independent events, the probability that both A and B occur is 1/8 are the probability that neither of them occours is 3/8. Find the probaility of the occurrence of A.

Let A and B be two events such that p( bar (AuuB))=1/6, p(AnnB)=1/4 and p( bar A)=1/4 , where bar A stands for the complement of the event A. Then the events A and B are (1) mutually exclusive and independent (2) equally likely but not independent (3) independent but not equally likely (4) independent and equally likely

If the events A and B are not mutually exclusive then P(A cup B) =