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 possible values of $X$ ?

• A. $9,7,4,0$
• B. $0,2,4,6$
• C. $6,7,7,2$
• D. $6,4,2,0$

Answer 1

The correct option is B $0,2,4,6$

A coin is tossed six times and $X$ 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 $X$ are $0,2,4$ and $6$.