Your roommate was having Skittles for lunch and they offer you some.

There are five different colors in a bag of Skittles: red, orange, yellow, green, and purple, and there are 20 of each color. You know your roommate is a huge fan of the green Skittles. With probability 1/2 they ate all of the green ones, with probability 1/4 they ate half of them, and with probability 1/4 they only ate 5 green ones.

a) If all three Skittles you took from the bag are green, what are the probabilities that your roommate had all of the green ones, half of the green ones, or only 5 green ones?
b) If you take three Skittles from the bag, what is the probability that they are all the same color?

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