Which statement correctly distinguishes the hypergeometric distribution from the binomial distribution?

• A. Hypergeometric models sampling with replacement; Binomial models without replacement.
• B. Hypergeometric assumes independent trials with constant probability; Binomial does not.
• C. Hypergeometric describes a continuous quantity; Binomial describes a discrete quantity.
• D. Hypergeometric describes the number of successes in draws without replacement from a finite population; Binomial describes the number of successes in independent trials.

Answer: (D)

The key idea is how sampling is performed. Hypergeometric distribution applies when you draw without replacement from a finite population, so each draw changes the mix of successes and failures and the trials are dependent. It counts how many successes you get in a fixed number of draws from that finite group.

Binomial distribution, on the other hand, describes the number of successes in a fixed number of independent trials, each with the same probability of success. This independence comes from sampling with replacement (or from an effectively infinite population where one draw doesn’t affect the next).

So the statement that hypergeometric describes the number of successes in draws without replacement from a finite population, while binomial describes the number of successes in independent trials, captures the essential difference between them.