Question

Find the probability of exactly five successes in seven trials of a binomial experiment in which the probability of success is 70%. Round to the nearest tenth of a percent.​

Answer 1

The probability of exactly five successes in seven trials of a binomial experiment with a probability of success of 70% is approximately 2.8%.

Step-by-step explanation:

To find the probability of exactly five successes in seven trials of a binomial experiment with a probability of success of 70%, we can use the binomial probability formula.

The formula is:

P(X=k) = nCk * p^k * (1-p)^(n-k)

where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the number of combinations of n items taken k at a time.

In this case, n = 7, k = 5, and p = 0.70.

Calculating:

P(X=5) = 7C5 * (0.70)^5 * (1-0.70)^(7-5)

P(X=5) = 21 * 0.16807 * 0.0081

P(X=5) = 0.0284767

So, the probability of exactly five successes in seven trials is approximately 0.0285, or 2.8% rounded to the nearest tenth of a percent.