# Is it true that non mutually exclusive events can only be independent events?

##### 1 Answer

#### Answer:

No. It is not always true. See explanation.

#### Explanation:

First we have to look at the definitions.

Two events **independent** if and only if

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:

**and** not more than

so:

Now let's check if the events are independent:

**not** independent.

**Conclusion:**

Example events are **not** mutualy exclusive and **not** independent, so it is a counter-example against hypothesis stated in the question.