Question

True or False, explain. If false, give counter example.

a) if events A and B disjoint then A and B independent.

b) if events A and B independent then A and B disjoint.

c) It is impossible for events A and B to be both mutually exclusive and independent.

Answer 1

If the events are disjoint, then P(A ∩ B)=0, so

P(A ∪ B) = P(A) +p(B)

For the intersection of two independent events, A and B,. P(A ∩ B)=p(A)p(B) for two independent events.

Two disjoint events can never be independent, except in the case that one of the events is null.Events are considered disjoint if they never occur at the same time

A and B being disjoint events implies that if event A occurs then B does not occur .

This implies that A and B are not independent.

a)Statement a is false.

b) false

c) true

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