Binomial-MM-Answers - a. They are all brown?...

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1 Problem 3 SU07 5-Jul-07 Problem 3 From Intro Stats by DeVeaux, Velleman, & Bock The Masterfoods company says that before the introduction of purple, yellow candies , red another 20%, and orange, blue, and green each made up 10%. The rest were brown. For all of the following problems, assume the batch is so large that picking one M&M doesn’t affect the individual probabilities when sampling is done without replacement. Show the formulas used to answer the following. a) If you pick an M&M at random, what is the probability that a. It is brown? P(x = brown) = 0.3 b. It is yellow or orange? P(x = yellow or orange ) = P(A) + P(B) = 0.2 +0.1 = 0.3 c. It is not green? P(x ≠ green) = 1 – P(x = green) = 1 0.1 = 0.9 d. It is striped? P(x = stripped) = 0 b) If you pick three M&M’s in a row, what is the probability that
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Unformatted text preview: a. They are all brown? (0.3)(0.3)(0.3) = 0.027 b. The third one is the first one that is red (the first two are not red)? (0.8)(0.8)(0.2) = 0.128 c. None are yellow? (0.8)(0.8)(0.8) = 0.512 d. At least one is yellow? 1 P(x = none are yellow) = 1 0.512 = 0.488 You have calculated the probabilities of getting various M&Ms based on the assumptions that the outcomes described were mutually exclusive. Other answers depended on the assumption that the events were independent. Do you understand the difference between mutually exclusive and independent? a) If you draw one M&M, are the events of getting a red one and getting an orange one mutually exclusive or independent or both or neither? Both: mutually exclusive and independent b) Can disjoint (mutually exclusive) events ever be independent? Explain. Yes -...
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