Final answer:
To find the probability that 2 out of 10 randomly chosen students have hardcover textbooks, we can use the binomial probability formula. The exact probability is 0.275 and the approximate probability using a binomial distribution is 0.305.
Step-by-step explanation:
To determine the probability that exactly 2 out of 10 randomly chosen students have hardcover textbooks, we can use the binomial probability formula. The formula is P(X=k) = C(n,k) * 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 C(n,k) represents the combination of n items taken k at a time.
For this problem, n = 10 (number of students chosen), k = 2 (number of students with hardcover textbooks), and p = 0.25 (probability of a student having a hardcover textbook). Using these values, we can calculate the exact probability:
P(X=2) = C(10,2) * 0.25^2 * (1-0.25)^(10-2) = 45 * 0.25^2 * 0.75^8 = 0.2748, or approximately 0.275.
To find the approximate probability using a binomial distribution, we can use a calculator or a binomial distribution table. Using the same values as above, we can calculate the approximate probability to be 0.305.