Question

Let $X$ represents the absolute value of difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. Then the possible values of $X$ are:

• A. $\{0,1,2,3,4,5,6\}$
• B. $\{0,1,2,3,4,5\}$
• C. $\{1,3,5\}$
• D. $\{0,2,4,6\}$

Answer 1

The correct option is D $\{0,2,4,6\}$

Given a coin is tossed $6$ times.
$X$ represents the difference between the number of heads and the number of tails.
$\Rightarrow X(6H,0T)=|6-0|=6$
$\Rightarrow X(5H,1T)=|5-1|=4$
$\Rightarrow X(4H,2T)=|4-2|=2$
$\Rightarrow X(3H,3T)=|3-3|=0$
$\Rightarrow X(2H,4T)=|2-4|=2$
$\Rightarrow X(1H,5T)=|1-5|=4$
$\Rightarrow X(0H,6T)=|0-6|=6$
Therefore, $X$ is a function on sample space whose range is $\{0,2,4,6\}.$
Thus, $X$ is a random variable which can take the value $0,2,4,$ or $6$.