# Negative binomial distribution

##### Intros
###### Lessons

1. • Deriving negative binomial distribution
• Formula for negative binomial distribution
• Relation of geometric distribution to the negative binomial distribution
##### 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?