Question

A binomial probability experiment is conducted with given parameters. Compute the probability of x successes in the n independent trials of the experiment.

N=15, p=0.2,×=4

Answer 1

P(X = 4) = 0.1876

Explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this question:

`n = 15, p = 0.2`

We want P(X = 4). So

`P(X = 4) = C_(15,4).(0.2)^(4).(0.8)^(11) = 0.1876`