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Hypergeometric Distribution quiz

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  • What is the main difference between the binomial and hypergeometric distributions?
    The binomial distribution assumes independent trials with constant probability, while the hypergeometric distribution involves dependent trials where probabilities change after each draw.
  • When do you use the hypergeometric distribution instead of the binomial distribution?
    You use the hypergeometric distribution when sampling is done without replacement, making the trials dependent.
  • What does 'without replacement' mean in the context of probability distributions?
    'Without replacement' means that once an item is drawn, it is not returned to the group, so it cannot be selected again in future draws.
  • In the hypergeometric distribution, what does the variable 'n' represent?
    'n' represents the number of draws or trials performed.
  • What does the variable 'r' stand for in the hypergeometric formula?
    'r' is the number of successes in the population at the start.
  • What does the variable 'N' (capital N) represent in the hypergeometric distribution?
    'N' is the total number of items in the population at the beginning.
  • How does the probability of success change in the hypergeometric distribution as items are drawn?
    The probability of success changes because each draw alters the composition of the remaining items, affecting future probabilities.
  • What is the denominator in the hypergeometric probability formula, and what does it represent?
    The denominator is 'N choose n', representing the total number of possible ways to draw 'n' items from 'N'.
  • What does the numerator in the hypergeometric probability formula calculate?
    The numerator calculates the number of ways to get the desired number of successes and failures in the draws.
  • How many outcomes are possible in each trial of a hypergeometric experiment?
    Each trial has two possible outcomes: success or failure.
  • Why can't you use the binomial formula when sampling without replacement?
    Because the probability of success changes after each draw, violating the binomial requirement of independent trials with constant probability.
  • What is the probability of drawing exactly one red marble in three draws from a bag with two red and four blue marbles, without replacement?
    The probability is 3/5.
  • What is the probability of drawing exactly one red marble in three draws from a bag with two red and four blue marbles, with replacement?
    The probability is 4/9.
  • Why is it recommended to memorize the hypergeometric formula?
    Because the formula can be difficult to derive, but straightforward to use once memorized.
  • What does 'r choose x' represent in the hypergeometric formula?
    'r choose x' represents the number of ways to choose 'x' successes from 'r' available successes in the population.