Question

A die is thrown. $A$ is the event that prime number comes up, $B$ is the event that the number divisible by three comes up, $C$ is the event that the perfect square number comes up. Then, $A,B$ and $C$ are :

• A. Mutually exclusive
• B. Mutually exhaustuve
• C. Same
• D. None of these

Answer 1

The correct option is B Mutually exhaustuve

Here, the sample space is $S=\{1,2,3,4,5,6\}$
$\Rightarrow n\left(S\right)=6$
$A$ : Getting a prime number $\Rightarrow A=\{2,3,5\}$
$\therefore n\left(A\right)=3$
$B$ : Getting a number divisible by $3\Rightarrow B=\{3,6\}$
$\therefore n\left(B\right)=2$
$C$ : Getting a perfect square $\Rightarrow C=\{1,4\}$
$\therefore n\left(C\right)=2$

Now, $A\cup B\cup C=\{1,2,3,4,5,6\}$
Thus, the events $A,B$ and $C$ are mutually exhaustive events.