Abinomial probability experiment is conducted with the given parameters. compute the probability of x successes in the n independent trials of the experiment.
n= 15, p=0.8, x = 12
p(12) =
(do not round until the final answer. then round to four decimal places as needed.)

Applying the binomial distribution, we get that P(X = 12) = 0.2501.

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Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, given by:

is the number of different combinations of x objects from a set of n elements, defined by the formula below.

Considering that p is the probability of a success on a single trial.

For this problem, the parameters are , and we want to find P(X = 12). Then:

Thus P(X = 12) = 0.2501.

A similar problem is given at link

The probability of getting 12 successes out of 15 trials is .

Step-by-step explanation:

Given:

The probability distribution is binomial distribution.

Number of trials are,

Number of successes are,

Probability of success is,

Therefore, probability of failure is,

Now, probability of getting 12 successes out of 15 trials is given as:

Therefore, the probability of getting 12 successes out of 15 trials is 0.2501.

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