Question

A bag contains $2$ white and $1$ red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If $X$ denotes the number of red balls recorded in the two draws, then range of $X$ is:

• A. $\{0,1\}$
• B. $\{1,2\}$
• C.
  $\{0,2\}$
• D. $\{0,1,2\}$

Answer 1

The correct option is D $\{0,1,2\}$

Let the balls in the bag be denoted by $w_1,w_2,r.$
Then the sample space is
$S\{w_1{w}_1,w_1{w}_2,w_2{w}_2,w_2{w}_1,w_{1}r,w_{2}r,r{w}_1,r{w}_2,rr\}$
Now, for $w\in S$
$X\left(w\right)=\text{number of red balls}$
Therefore
$X\left(w\right)$ can be $0$ or $1$ or $2$
Thus, $X$ is a random variable which can take values $\{0,1,2\}$