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Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 1 3 4 p(y) 0.55 0.24 0.13 0.05 (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret p(1) = 0.24? (c) Calculate P(y s 2), the probability that the carton contains at most two broken eggs. Interpret this probability. (d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. Why is this smaller than the probability in part (c)?

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 1 3 4 p(y) 0.55 0.24 0.13 0.05 (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret p(1) = 0.24? (c) Calculate P(y s 2), the probability that the carton contains at most two broken eggs. Interpret this probability. (d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. Why is this smaller than the probability in part (c)?

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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Please answer part b,c, and d

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. 1 3 4 p(y) 0.55 0.24 0.13 0.05 (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret p(1) = 0.24? (c) Calculate P(y < 2), the probability that the carton contains at most two broken eggs. Interpret this probability. (d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. Why is this smaller than the probability in part (c)?
Transcribed Image Text:Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. 1 3 4 p(y) 0.55 0.24 0.13 0.05 (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) (b) How would you interpret p(1) = 0.24? (c) Calculate P(y < 2), the probability that the carton contains at most two broken eggs. Interpret this probability. (d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. Why is this smaller than the probability in part (c)?
(b) How would you interpret p(1) = 0.24? The probability distribution of a discrete random variable y gives the probability associated with each possible y value. Each probability is the long run relative frequency of occurrence of the corresponding y value when a chance experiment is performed a very large number of times. The notation p(1) represents the probability that the random variable y takes on the value 1. Thus, p(1) = 0.24 indicates the following. O In the long run, the proportion that will have at most one broken egg will equal 0.24. O The proportion of eggs that will be broken in each carton from this population is 0.24. O The probability of one randomly chosen carton having broken eggs in it is 0.24. O In the long run, the proportion of cartons that have exactly one broken egg will equal 0.24.
Transcribed Image Text:(b) How would you interpret p(1) = 0.24? The probability distribution of a discrete random variable y gives the probability associated with each possible y value. Each probability is the long run relative frequency of occurrence of the corresponding y value when a chance experiment is performed a very large number of times. The notation p(1) represents the probability that the random variable y takes on the value 1. Thus, p(1) = 0.24 indicates the following. O In the long run, the proportion that will have at most one broken egg will equal 0.24. O The proportion of eggs that will be broken in each carton from this population is 0.24. O The probability of one randomly chosen carton having broken eggs in it is 0.24. O In the long run, the proportion of cartons that have exactly one broken egg will equal 0.24.
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