Q.4.5 - A First Course in Probability

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?

Step-by-Step Solution

Answer

Possible values of X  can be described by:

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

Step 1 : Given Information

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

Step 2 : 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:

 $X=h-t=n-t-t=n-2 t$

All possible outcomes of X can be described as below:

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

                     

Step 3 : Final Result

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