Question

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

Short answer

Possible values of X can be described by:

$\{n-2t\mid t\in \{0,1,\dots ,n\left\}\right\}$

Step-by-step solution

Step1:Given Information

X - It is the difference between the number of heads and the number of tails.

Step2:Explanation

Possible outcomes of X, when a coin is tossed n times are:

If the number of tails is t, then the number of heads(h) is n-t.

$h=n-t$

Therefore X can be written as:

$X=h-t=n-t-t=n-2t$

All possible outcomes of X can be described as below:

$\{n-2t\mid t\in \{0,1,\dots ,n\left\}\right\}$

Step3: Final Result

Possible values of X are given below: $\{n-2t\mid t\in \{0,1,\dots ,n\left\}\right\}$