00:01
In this question, let n denote the total number of tosses till a head appears.
00:17
Thus, the probabilities here are computed as p of n is equal to 1 is equal to 0 .5 and p of n is equal to 2 is equal to 0 .5 multiplied by 0 .5 which is equal to 0 .5 square and so on till we have p of n is equal to n will be equal to 0 .5 power n.
00:39
Therefore, the probability here is computed as p of x equal to 0 will be equal to p of n is equal to 1 multiplied by p of x equal to 0 such that n is equal to 1 plus p of n is equal to 2 multiplied by p of x equal to 0 over n is equal to 2 and so on.
01:04
So, we have p of x equal to 0 value is equal to 0 .5 multiplied by 0 .5 plus 0 .5 square multiplied by 0 .5 square plus 0 .5 cube multiplied by 0 .5 cube plus so on till infinity.
01:22
So, from this we can conclude p of x equal to 0 will be equal to 0 .5 square plus 0 .5 power 4 plus 0 .5 power 6 and so on in infinity.
01:36
Using the sum of an infinite gp we have p of x equal to 0 will be equal to 0 .5 square divided by 1 minus 0 .5 square.
01:47
This is nothing but using the sum of an infinite gp which is equal to 0 .25 divided by 0 .75.
01:55
Therefore, we get the value of p of x equal to 0 is equal to 1 over 3.
02:00
This is the required value of p of x equal to 0...