Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange,...

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. Suppose it is claimed that the color proportions 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 that there are exactly two M&Ms of each color? (Round your answer to four decimal places.) Correct: Your answer is correct. (b) For n = 20, what is the probability that there at most eight orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.] (Round your answer to three decimal places.) (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 8? (Round your answer to three decimal places.)

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milcah answered 5 months ago

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