Exercise 8.9 A restaurant sells three different types of dessert: chocolate, brownies, yogurt with seasonal fruits, and lemon tart. Years of experience have shown that the probabilities with which the desserts are chosen are 0.2, 0.3, and 0.5, respectively. (a) What is the probability that out of 5 guests, 2 guests choose brownies, I guest chooses yogurt, and the remaining 2 guests choose lemon tart? (b) Suppose two out of the five guests are known to always choose lemon tart. What is the probability of the others choosing lemon tart as well? (c) Determine the expectation and variance assuming a group of 20 guests.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Exercise 8.9 A restaurant sells three different types of dessert: chocolate, brownies,
yogurt with seasonal fruits, and lemon tart. Years of experience have shown that the
probabilities with which the desserts are chosen are 0.2, 0.3, and 0.5, respectively.
(a) What is the probability that out of 5 guests, 2 guests choose brownies, I guest
chooses yogurt, and the remaining 2 guests choose lemon tart?
(b) Suppose two out of the five guests are known to always choose lemon tart. What
is the probability of the others choosing lemon tart as well?
(c) Determine the expectation and variance assuming a group of 20 guests.
Transcribed Image Text:Exercise 8.9 A restaurant sells three different types of dessert: chocolate, brownies, yogurt with seasonal fruits, and lemon tart. Years of experience have shown that the probabilities with which the desserts are chosen are 0.2, 0.3, and 0.5, respectively. (a) What is the probability that out of 5 guests, 2 guests choose brownies, I guest chooses yogurt, and the remaining 2 guests choose lemon tart? (b) Suppose two out of the five guests are known to always choose lemon tart. What is the probability of the others choosing lemon tart as well? (c) Determine the expectation and variance assuming a group of 20 guests.
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