Question

A poll is given, showing 55 % are in favor of a new building project. If 10 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

Answer 1

To find the probability that exactly 4 out of 10 people favor the new building project, we need to use the binomial probability formula. The probability is approximately 0.2277, or 22.77%.

Step-by-step explanation:

To find the probability that exactly 4 out of 10 people favor the new building project, we need to use the binomial probability formula. The formula is:

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

In this case, n = 10 (number of people chosen), k = 4 (number of people favoring the project), and p = 0.55 (percentage in favor). Plugging these values into the formula, we get:

P(X = 4) = C(10, 4) * 0.55^4 * (1 - 0.55)^(10 - 4)

To calculate C(10, 4), which represents the number of combinations of choosing 4 out of 10 people, we can use the formula C(n, k) = n! / (k! * (n - k)!). In this case, C(10, 4) = 10! / (4! * (10 - 4)!).

Using a calculator or factorial function, we can find C(10, 4) = 210.

Now we can substitute the values into the binomial probability formula:

P(X = 4) = 210 * 0.55^4 * (1 - 0.55)^(10 - 4)

Calculating this expression, we find that the probability that exactly 4 out of 10 people favor the new building project is approximately 0.2277, or 22.77%.