Question

Consider a binomial experiment with n = 10 and p = 0.20. What is the probability of getting exactly 3 successes?

1) 0.201
2) 0.268
3) 0.2013
4) 0.2684

Answer 1

The probability of getting exactly 3 successes in a binomial experiment with n = 10 and p = 0.20 is 0.2684.

Step-by-step explanation:

To find the probability of getting exactly 3 successes in a binomial experiment with n = 10 and p = 0.20, we can use the binomial probability formula. The formula is:

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

Where n is the number of trials, p is the probability of success, k is the number of successes we want to find the probability for, and (n choose k) represents the number of ways to choose k successes from n trials.

In this case, n = 10, p = 0.20, and k = 3. Substituting these values into the formula, we get:

P(X = 3) = (10 choose 3) * (0.20)^3 * (0.80)^(10-3)

Using calculations, we find that (10 choose 3) = 120. Plugging this value and the given probabilities into the formula:

P(X = 3) = 120 * (0.20)^3 * (0.80)^(10-3) = 0.2684

Therefore, the probability of getting exactly 3 successes is 0.2684.