Negative binomial distribution

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Intros
Lessons

  1. • Deriving negative binomial distribution
    • Formula for negative binomial distribution
    • Relation of geometric distribution to the negative binomial distribution
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Examples
Lessons
  1. Identifying Negative Binomial Distributions
    Identify which of the following experiments below are negative binomial distributions?
    i.
    A fair coin is flipped until head comes up 4 times. What is the probability that the coin will be flipped exactly 6 times?
    ii.
    Cards are drawn out of a deck until 2 exactly aces are drawn. What is the probability that a total of 10 cards will be drawn?
    iii.
    An urn contains 3 red balls and 2 black balls. If 2 balls are drawn with replacement what is the probability that 1 of them will be black?
    iv.
    Roll a die until the first six comes up. What is the probability that this will take 3 rolls?
    1. Determining the Negative Binomial Distribution
      A fair coin is flipped until head comes up 4 times. What is the probability that the coin will be flipped exactly 6 times?
      1. Determining the Cumulative Negative Binomial Distribution
        A sculptor is making 3 exhibits for an art gallery. There is a probability of 0.75 that every piece of wood she carves into will be good enough to be part of the exhibit. What is the probability that she uses 4 pieces of wood or less?