Let the two events be $A$ and $B$.The condition for both to be mutually exclusive is that their intersection should be a null set and the condition for independence is that their intersection should be equal to the product of the two probabilities. Now how do I proceed? Or do I just have to write that if the the events are both mutually exclusive and independent then one of the events will have zero probability ?

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  • Consider the value of $P(A\cap B)$. If $A$ and $B$ were mutually exclusive, what should this be equal to? If $A$ and $B$ were independent and each occur with nonzero probability, could this be equal to what we had before? – JMoravitz May 29 '20 at 13:52
  • Yes it does. Does it mean that I can use what I have written in the body of the question as proof for the question asked in the title ? – Slothrop May 29 '20 at 15:22

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