For a binomial distribution with a sample size equal to 10 and a probability of a success equal to 0.30, what is the probability that the sample will contain exactly three successes? use the binomial formula to determine the probability. round to four decimal places.

Using the binomial distribution, it is found that there is a 0.2668 = 26.68% probability that the sample will contain exactly three successes.

The formula is:

The parameters are:

In this problem:

The probability that the sample will contain exactly three successes is P(X = 3), hence:

More can be learned about the binomial distribution at link

The probability that the sample will contain exactly three successes is 0.2668.

Step-by-step explanation:

Given information:

Sample size = 10

Probability of a success, p=0.30

Probability of a failure q=1-p = 1-0.30 = 0.70

The binomial formula to determine the probability is

where, n is the sample size, r is required number of success, p is probability of success and q is probability of failure.

We need to find the probability that the sample will contain exactly three successes.

Therefore the probability that the sample will contain exactly three successes is 0.2668.

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