Is there any relation between a independece of a event and a mutual exclusive event?

Question

This questions was proposed by our statistics teacher as home work.

I have been looking for any reasonable explanation but so far I am getting more and more confused differentiating between the two concepts.

Could someone please clarify them for me?

Answer 1

If A and B are independent $$P(A \cap B)=P(A)P(B)$$

If they are mutually exclusive then $$P(A \cap B)=0$$

So the only way that two outcomes can be both independent and mutually exclusive is if at least one of the outcomes occurs with zero probability