Question

Three coins are tossed. Describe two events $A$ and $B$ which are mutually exclusive but not exhaustive.

Answer 1

When three coins are tossed, the sample space is given by

$S=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT$

Two events that are mutually exclusive can be

Let A be the event of getting only heads and B be the event of getting only tails

Then $A=HHHandB=TTT$

So, $A\cap B=\varphi$

Since no element is common in A bad B.

Hence A and B are mutually exclusive.