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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Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.
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?
Consider an experiment in which a person from Valdosta State is selected at random. Let E be the event that the person selected has brown hair, and let F be the event that the person selected is female. Which of the following notations would indicate the probability that the person from Valdosta state has brown hair, given that the person is female?
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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.