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Urn A contains one red ball and four white balls and Um B contains three red balls and one white ball. Two balls are randomly drawn from Ur A and placed into Ur B, then two balls are randomly drawn from Urn B and returned to Urn A. a) Calculate the probability that both urns contain the same distribution of red and white balls after the draws as they did before the draws. b) The process described in the preamble to Question 3 is followed. Then, five balls are drawn from Urn B with replacement and the number of red balls drawn is noted. If the number of red balls drawn is two, calculate is the probability that Urn B contains the same distribution of red and white balls as it did in the beginning?

Urn A contains one red ball and four white balls and Um B contains three red balls and one white ball. Two balls are randomly drawn from Ur A and placed into Ur B, then two balls are randomly drawn from Urn B and returned to Urn A. a) Calculate the probability that both urns contain the same distribution of red and white balls after the draws as they did before the draws. b) The process described in the preamble to Question 3 is followed. Then, five balls are drawn from Urn B with replacement and the number of red balls drawn is noted. If the number of red balls drawn is two, calculate is the probability that Urn B contains the same distribution of red and white balls as it did in the beginning?

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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Urn A contains one red ball and four white balls and Um B contains three red balls and one white ball. Two balls are randomly drawn from Ur A and placed into Ur B, then two balls are randomly drawn from Urn B and returned to Urn A. a) Calculate the probability that both urns contain the same distribution of red and white balls after the draws as they did before the draws. b) The process described in the preamble to Question 3 is followed. Then, five balls are drawn from Urn B with replacement and the number of red balls drawn is noted. If the number of red balls drawn is two, calculate is the probability that Urn B contains the same distribution of red and white balls as it did in the beginning?
Transcribed Image Text:Urn A contains one red ball and four white balls and Um B contains three red balls and one white ball. Two balls are randomly drawn from Ur A and placed into Ur B, then two balls are randomly drawn from Urn B and returned to Urn A. a) Calculate the probability that both urns contain the same distribution of red and white balls after the draws as they did before the draws. b) The process described in the preamble to Question 3 is followed. Then, five balls are drawn from Urn B with replacement and the number of red balls drawn is noted. If the number of red balls drawn is two, calculate is the probability that Urn B contains the same distribution of red and white balls as it did in the beginning?
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