et X,, X2, X3, X, X5, and X, denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these ;s have a multinomial distribution. Suppose it is claimed that the color proportions are p, = 0.25, P2 = 0.13, p3 = 0.15, P4 = 0.2, P5 = 0.12, and Pe = 0.15. In USE SALT (a) If n = 12, what is the probability that there are exactly tvwo M&Ms of each color? (Round your answer to four decimal places.) (b) For n = 25, what is the probability that there at most four 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 25 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 11? (Round your answer to three decimal places.)
et X,, X2, X3, X, X5, and X, denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these ;s have a multinomial distribution. Suppose it is claimed that the color proportions are p, = 0.25, P2 = 0.13, p3 = 0.15, P4 = 0.2, P5 = 0.12, and Pe = 0.15. In USE SALT (a) If n = 12, what is the probability that there are exactly tvwo M&Ms of each color? (Round your answer to four decimal places.) (b) For n = 25, what is the probability that there at most four 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 25 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 11? (Round your answer to three decimal places.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Let X,, X, X3, X4 X5, and Xg denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these
x;s have a multinomial distribution. Suppose it is claimed that the color proportions are p, = 0.25, P2 = 0.13, P3 = 0.15, P4 = 0.2, P5 = 0.12, and Pe = 0.15.
%3D
A USE SALT
(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.)
(b) For n = 25, what is the probability that there at most four 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 25 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 11? (Round your answer to
three decimal places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8536f70-6afb-49b2-94d8-7d5f9820999c%2F72eb134d-6490-43c5-834a-5a28968eeda3%2Fwfvfki_processed.png&w=3840&q=75)
Transcribed Image Text:Let X,, X, X3, X4 X5, and Xg denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these
x;s have a multinomial distribution. Suppose it is claimed that the color proportions are p, = 0.25, P2 = 0.13, P3 = 0.15, P4 = 0.2, P5 = 0.12, and Pe = 0.15.
%3D
A USE SALT
(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.)
(b) For n = 25, what is the probability that there at most four 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 25 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 11? (Round your answer to
three decimal places.)
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