Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X=3), n=8, p=0.2

Answer 1

P(X = 3) = 0.14680064

Explanation:

Formula=============================

`p\left( X=k\right) =C^(k)_(n)p^(k)(1-p)^(n-k)\ \ ;\ k\in \left\{ 0,\ldots ,n\right\}`

……………………………………………………………………..

Given :

n = 8

p = 0.2

1 - p = 1 - 0.2 = 0.8

k = 3

Then

`p\left( X=3\right) =C^(3)_(8)(0.2)^(3)(0.8)^(5)`

`=0.14680064`