Skittles candies come in the colors red, orange, yellow, green, and purple, with each color having equal

Question:

Skittles candies come in the colors red, orange, yellow, green, and purple, with each color 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 first rainbow-striped candy coming down the line. (The population is so big that 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 Geometric situation? What is the parameter?
c. What is the probability that you will need to check exactly 10 candies to find the first rainbow one?
d. What is the probability that you will have to check fewer than 12 candies to find the first rainbow one?
e. What is the probability you will have to check more than 8 candies to find the first rainbow one?
f. Given that you have to check at least 3 candies, what is the probability that you will need to check a total of more than 9 for the first rainbow one?
g. What is the expected number of candies you will have to check until you find the first rainbow one?
h. What is the standard deviation in the number of candies you will have to check until you find your first rainbow one? Distribution
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