# Are mutually exclusive events dependent?

**mutually exclusive**)

**events**are always

**dependent**since if one

**event**occurs we know the other one cannot.

Also asked, can an event be independent and mutually exclusive?

**Mutually exclusive events** cannot happen at the same time. For example: when tossing a coin, the result **can** either be heads or tails but cannot be both. This of course means **mutually exclusive events** are not **independent**, and **independent events** cannot be **mutually exclusive**. (**Events** of measure zero excepted.)

**test**whether two

**events**A and B are independent, calculate P(A), P(B), and P(A ∩ B), and then check whether P(A ∩ B) equals P(A)P(B).

**If**they are equal, A and B are independent;

**if**not, they are

**dependent**.

In this manner, are mutually exclusive or disjointed events independent or dependent?

**Events** are considered **disjoint** if they never occur at the same time; these are also known as **mutually exclusive events**. **Events** are considered **independent** if they are unrelated. Two **events** that do not occur at the same time.

Two events are said **to** be **mutually exclusive**, when **their** occurrence is not simultaneous. Two events are said **to** be **independent**, when **the** occurrence **of** one event cannot control **the** occurrence **of** other. Occurrence **of** one event will result in **the** non-occurrence **of the** other.