Is it true that non mutually exclusive events can only be independent events?
1 Answer
No. It is not always true. See explanation.
Explanation:
First we have to look at the definitions.
Two events
Two events are mutualy exclusive if their product is empty set
(i.e.
Let's consider 2 events with throwing a 6 sided die.
These 2 events are not mutualy exclusive because their product is:
so:
Now let's check if the events are independent:
Conclusion:
Example events are not mutualy exclusive and not independent, so it is a counter-example against hypothesis stated in the question.