Skittles candies come in the colors red, orange, yellow, green, and purple, with each of these colors

Question:

Skittles candies come in the colors red, orange, yellow, green, and purple, with each of these colors having equal probability. Due to a dye mix-up there are a few rainbow-striped candies coming down the line. There is a 5% chance that a candy is rainbow striped. You are a quality control inspector, and your job is to find the 3rd rainbow-striped candy. (The population is so big, and we randomly sample the Skittles, so we can assume relative independence.)
a. Explain in words what X is in terms of the story. What values can it take?
b. Why is this a Negative Binomial situation? What are the parameters?
c. What is the probability that you will need to check exactly 20 candies to find the 3rd rainbow one?
d. What is the probability that you will have to check fewer than 6 candies to find the 3rd rainbow one?
e. What is the probability you will have to check more than 6 candies to find the 3rd rainbow one?
f. What is the expected number of candies you will have to check to find the 3rd rainbow one?
g. What is the standard deviation of the number of candies you will have to check to find your 3rd rainbow one? Distribution
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