Question

If $E_1,E_2,E_3\dots E_n$ are n events of a sample space S and if $E_1\cup E_2\cup E_3\cup \dots E_n=S$, then $E_1,E_2\dots E_n$ are called mutually exclusive and exhaustive events.

• A. True
• B. False

Answer 1

The correct option is B

False

We say two events are mutually exclusive if they have no outcome in common or $A\cap B=\varphi$.

For more than two events to be mutually exclusive each pair should be mutually exclusive. We are not given any information of this sort in the question. So, they can be mutually exclusive or not mutually exclusive. So saying that they are mutually exclusive is wrong.

We say a set of events $E_1,E_2,E_3\dots E_n$ are exhaustive, if their combination gives sample space S.

i.e., $E_1\cup E_2\cup E_3\dots E_n=S$

So they are Exhaustive