Final answer:
Using binomial distribution, calculate the probabilities of exactly 0 and exactly 1 student being in a relationship and subtract from 1 to find the probability of at least 2 students in a committed relationship in a sample of 10 students.
Step-by-step explanation:
The student's question pertains to the concept of probability specific to binomial distributions. In a scenario where there is a 30% chance of an individual college student being in a committed relationship, we are asked to find the probability that in a sample of 10 independent students, at least 2 will be in a committed relationship. Using the concept of binomial distribution, we can calculate the probability of exactly 0 and exactly 1 student being in a relationship and subtract these probabilities from 1 to find the probability of at least 2 students being in a relationship.
The formula for calculating the probability in a binomial distribution is:
P(X = k) = (n choose k) * (p)^k * (1-p)^(n-k)
Where 'n' is the number of trials (students), 'k' is the number of successes (students in a relationship), and 'p' is the probability of a single success. We calculate P(X = 0) and P(X = 1), and then use this information as follows:
P(at least 2) = 1 - P(X = 0) - P(X = 1)