If A and B are independent events each with positive probability, prove that they cannot be mutually exclusive. Not to sure about this one but this is what I have: This is all I have.
Follow Math Help Forum on Facebook and Google+
Originally Posted by dwsmith If A and B are independent events each with positive probability, prove that they cannot be mutually exclusive. Not to sure about this one but this is what I have: This is all I have. Okay so, The events are mutually exclusive if . Here you have are both greater than 0, so .
Originally Posted by harish21 Okay so, The events are mutually exclusive if . Here you have are both greater than 0, so . Proof by contradiction: We have reached a contradiction since . Therefore, A and B cannot be mutually exclusive.