True or False If false explain why it is false If two events

True or False? If false, explain why it is false.

If two events A and B are independent, then they are necessarily disjoint with A B =

Solution

Not necessarily. If two events are independent then it means that occurence of one event by no mean it affects the occurence of the other. As for an example consider the experiment of tossing a fair coin .

If we define two events

A= heads on two successive toss

B= tails on two successive toss.

Note that occurence of heads on two successive toss by no means affects the occurence of two tails in two sucessive toss. Hence A and B are indpendent.