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According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M's from an extra-large bag of the candies. What is the probability that exactly two of the six M&M's are orange? What is the probability that two or three of the six M&M's are orange? What is the probability that at most two of the six M&M's are orange?

According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M's from an extra-large bag of the candies. What is the probability that exactly two of the six M&M's are orange? What is the probability that two or three of the six M&M's are orange? What is the probability that at most two of the six M&M's are orange?

A First Course in Probability (10th Edition)
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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Question
5. Help please
According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M's from an extra-large bag of the candies. What is the probability that exactly two of the six M&M's are orange? What is the probability that two or three of the six M&M's are orange? What is the probability that at most two of the six M&M's are orange? What is the probability that at least two of the six M&M's are orange? If you repeatedly select random samples of six peanut M&M's, on average how many do you expect to be orange? orange M&M's With what standard deviation? orange M&M's
Transcribed Image Text:According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M's from an extra-large bag of the candies. What is the probability that exactly two of the six M&M's are orange? What is the probability that two or three of the six M&M's are orange? What is the probability that at most two of the six M&M's are orange? What is the probability that at least two of the six M&M's are orange? If you repeatedly select random samples of six peanut M&M's, on average how many do you expect to be orange? orange M&M's With what standard deviation? orange M&M's
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(5) Given,

Probability of M&M's are orange = 23%

That is, probability of success, p = 23% = 0.23

Sample size, n = 6

Let X = Number of M&M's are orange.

Using formula (Binomial distribution)

P left parenthesis X equals r right parenthesis equals C presuperscript n subscript r cross times left parenthesis p right parenthesis to the power of r cross times left parenthesis 1 minus p right parenthesis to the power of n minus r end exponent

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