Answer:
[tex]P(X = 5) = C_{30,5}.(0.2)^{5}.(0.8)^{25} = 0.172[/tex]
Step-by-step 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[\tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem, we have that:
[tex]n = 30, p = \frac{1}{5} = 0.2[/tex]
Use the binomial probability formula to find the probability of xequals5 successes given the probability pequalsone fifth of success on a single trial.
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{30,5}.(0.2)^{5}.(0.8)^{25} = 0.172[/tex]
