Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these Xi’s have a multinomial distribution. According to the M&M Web site, the color proportions are p1 =.24, p2 = .13, p3 = .16,
p 4 = .20, p5 = .13, and p6 = .14.
a. If n =12, what is the probability that there are exactly two M&Ms of each color?
b. For n = 20, what is the probability that there are at most five orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.]
c. In a sample of 20 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 10?
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