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 amultinomial distribution. Suppose it is claimed that the colorproportions are p1 = 0.22, p2 = 0.13, p3 = 0.18, p4 = 0.2, p5 =0.13, and p6 = 0.14. (a) If n = 12, what is the probability thatthere are exactly two M&Ms of each color? (Round your answer tofour decimal places.) Correct: Your answer is correct. (b) For n =20, what is the probability that there at most eight orangecandies? [Hint: Think of an orange candy as a success and any othercolor as a failure.] (Round your answer to three decimal places.)(c) In a sample of 20 M&Ms, what is the probability that thenumber of candies that are blue, green, or orange is at least 8?(Round your answer to three decimal places.)
