# Math Help - Independent events

1. ## Independent events

Hi there could anyone help me?

True/false
1) If events A and B are independent, then P (A & B) = P(A)P(B)
2) It is possible for two independent events with positive probabilities to be mutually exclusive

Thanks!

2. Originally Posted by iamterribleatmaths
Hi there could anyone help me?

True/false
1) If events A and B are independent, then P (A & B) = P(A)P(B)
2) It is possible for two independent events with positive probabilities to be mutually exclusive

Thanks!
1) T
2) F

The second is false because of the first property. Mutually exclusive means $P(A \cap B) = 0$, but if two events are independent, then $P(A \cap B) = P(A)*P(B)$, so if both probabilities are non-zero, then the events are not mutually exclusive.

3. Originally Posted by iamterribleatmaths
Hi there could anyone help me?

True/false
1) If events A and B are independent, then P (A & B) = P(A)P(B) Mr F says: True by definition, as your textbook and/or notes would surely say.

2) It is possible for two independent events with positive probabilities to be mutually exclusive Mr F says: False. By definition, Pr(A & B) = 0 if A and B are mutually exclusive events. But if A and B are independent events with positive probabilities, Pr(A & B) = Pr(A) Pr(B) neq 0 ....

Thanks!
..