Answer:
The probability is [tex]P(X = 5) = 142506*p^{5}*(1 - p)^{25}[/tex], in which p is the probability of a success on a single trial.
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.
The trial is repeated 30 times:
This means that [tex]n = 30[/tex]
Find the probability of 5 successes given the probability p of success on a single trial
This is [tex]P(X = 5)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{30,5}.p^{5}.(1 - p)^{25}[/tex]
[tex]P(X = 5) = 142506*p^{5}*(1 - p)^{25}[/tex]
The probability is [tex]P(X = 5) = 142506*p^{5}*(1 - p)^{25}[/tex], in which p is the probability of a success on a single trial.
