Question

Let $X$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $6$ times. What are the possible values of $X$?

Answer 1

Given : A coin is tossed $6$ times, then possible outcomes are

S = {$6$ tails and $0$ head, $5$ tails and $1$ head, $4$ tails and $2$ heads, $3$ tails and $3$ heads, $2$ tails and $4$ heads, $1$ tail and $5$ heads, $0$ tails and $6$ heads}

$X$: Represents the difference between the number of heads and the number of tails.

$\therefore X(6H,0T)=|6-0|=6$

$X(5H,1T)=|5-1|=4$

$X(4H,2T)=|4-2|=2$

$X(3H,3T)=|3-3|=0$

$X(2H,4T)=|2-4|=2$

$X(1H,5T)=|1-5|=4$

$X(0H,6T)=|0-6|=6$

Thus, the possible values of $X\text{are}6,4,2\&0.$