About 60% of US full-time college students drink alcohol within a one month period. You randomly select six US full-time college students. Find the probability that the number of US full-time college students who drink alcohol with a one month Is exactly 2.

This is a binomial probability problem, where we have a fixed number of trials (n = 6), a fixed probability of success (p = 0.6), and we want to find the probability of a certain number of successes (k = 2). The formula for binomial probability is: P(X=k) = \binom{n}{k}p^k(1-p)^{n-k} where $\binom{n}{k}$ is the binomial coefficient that represents the number of ways to choose k successes out of n trials. We can use this formula to calculate the probability as follows: P(X=2) = \binom{6}{2}(0.6)^2(1-0.6)^{6-2} P(X=2) = \frac{6!}{2!(6-2)!}(0.6)^2(0.4)^4 P(X=2) = \frac{720}{2\times 24}(0.36)(0.0256) P(X=2) = 15\times 0.009216 P(X=2) = 0.13824 Therefore, the probability that exactly 2 out of 6 US full-time college students drink alcohol within a one month period is **0.13824** or **13.824%**. You can learn more about binomial distribution from these sources¹²³⁴.