00:01
Hello students, here let x be a random variable denoting the number of success in 8 serves.
00:28
According to the question, the serves are independent to each other.
00:32
Therefore, x follows a binomial distribution of 8 .0 .61.
00:41
So therefore, the pmf of x is f x of x is f x of x is, equal to 8cx multiplied by 0 .61 to the power x multiplied by 0 .39 to the power 8 minus x where x is equal to 0128.
01:11
So in the first sub question we are asked to find p of x equal to 8.
01:16
So that will be equal to 8c8 multiplied by 0 .61 to the power 8.
01:24
By 0 .39 to the power 8 minus 8 which is 0.
01:29
Now this will be equal to 0 .0192.
01:40
So a required probability is 0 .0192.
01:44
Now for the second sub -question we have to find the probability that he or she gets exactly 2 cells.
01:50
That is we have to find p of x equal to 2 which will be equal to 8c2 multiplied by 0 .6 1.
01:59
To the power 2 multiplied by 0 .39 to the power 8 minus 2 which is 6.
02:05
Now on simplification this will be equal to 0 .0367 which is our required probability.
02:14
Now for the third sub -question we have to find the probability that he or she gets at least 6 serves...