##### Random Variable Example(2)

let us say we are flipping a coin and p is the probability of getting head and (1-p) is the probability of getting a tail and N is a random variable that counts the number of times coin is flipped until we get first time head.

What is the probability of getting first time head in the fourth flip?

**Answer**

With this question, we will understand the important concept of random variables.

The possible values that N can have are {1,2,3,4,5,6......} Why?

If we get Head as we flip first time then N=1

If we get head on the second flip then N= 2

If we get head on the third flip then N= 3 and so on

We can assign probability as:

P(N=1) = {H} = p

P(N=2)={TH} = (p-1)p

P(N=3) = {TTH}= (p-1)(p-1)(p)

P(N=4)={TTTH} =(p-1)(p-1)(p-1)(p) // because getting head or tail is independent event so we can directly write it like this.