Question: Discuss the assumptions and challenges involved in the following standard definition forprobability: Consider an experiment with the set of all outcomes S. Let ACS be an event. Then, theprobability of event A happening is P(A) = , where | · | denotes the cardinality of a set.

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Answered: Question: Discuss the assumptions and…

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.4 Using the axioms of probability and verify (prove that) P(A) < P(B) if A CB (NOTE: A Venn diagram will be drawn for proof ). 10 points.
From experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.70 of typical weather, 0.20 of unusually dry weather, and 0.10 of a severe storm. Let X denote the farmer's profit next year (a) Construct a table with the probability distribution of X. (b) What is the probability that the profit is $50,000 or less? (c) Find the mean of the probability distribution of X. Interpret. (d) Suppose the farmer buys insurance for $3000 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing otherwise. Find the probability distribution of his profit. Find the mean and summarize the effect of buying this insurance.
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Part 1: Suppose that F and X are events from a common sample space with P(F) # 0 and P(X) # 0. Prove that P(X) = P(X|F)P(F) + P(X|F)P(F). Hint: Explain why P(X|F)P(F) = P(Xn F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Theorem 4.1.1. %3D Explain why P(F|X) = P(X|F)P(F)/P(X) is another way of stating Theorem 4.2.1 Bayes Theorem.
Consider the following probability model, for the number of cars in American households (see attached image): We suppose, for the sake of this question, that there are no households in America with more than 6 cars (a) Is this a valid probability model? Check that the values in the table satisfy the two Probability Rules. (b) What proportion of American households don’t have zero cars (i.e., they have at least one car)? Show your work. (c) A developer builds townhouses with two-car garages. What proportion of American households have more cars than this garage can hold? (d) You pick an American household at random. What is the probability that this household has an odd number of cars?
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Question: Discuss the assumptions and challenges involved in the following standard definition for probability: Consider an experiment with the set of all outcomes S. Let A C S be an event. Then, the probability of event A happening is P(A) = , where | | denotes the cardinality of a set.