Final answer:
The random variable X represents the number of DVDs rented by a customer. To find the probabilities, use the hypergeometric probability formula and sum up the probabilities for specific ranges of X.
Step-by-step explanation:
The random variable X in this question represents the number of DVDs rented by a customer.
To find the probability that a customer rents three DVDs, you need to use the hypergeometric probability formula: P(X = x) = (N_1C_x * N_2C_(n-x)) / (N_C_n), where N_1 is the size of the first group, N_2 is the size of the second group, C is the combination function, and n is the total number of trials.
To find the probability that a customer rents at least four DVDs, you need to sum up the probabilities for X = 4, 5, 6, ..., up to the maximum possible value for X.
To find the probability that a customer rents at most two DVDs, you need to sum up the probabilities for X = 0, 1, and 2.