Question

26.9 Prove that if eventsAand B are disjoint and both have nonzero probability, then they are dependent

Answer #1

Solution :

Let two events A and B are disjoint. This means;

Also we have been given that;

Note that any two events are either independent or dependent. If two events C and D are independent then these two events follows;

For events A and B we have;

Since both the events has non zero probabilities.

And hence we get;

So A and B are not independent implies that both are dependent.

Prove
(a). Events A and B are independent if and only if Ac
and Bc are independent.
(b). If events A and B both have a positive probability and are
disjoint, then they cannot be independent.

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Prove that if p is prime then Zp, where it is nonzero, is a
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