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Statistics / Introduction to Probability, 2 / Chapter 1 / Problem 22

Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis

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Each of k jars contains m white and n black balls. A ball

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QUESTION:

Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, then a ball is randomly chosen from jar 2 and transferred to jar 3, etc. Finally, a ball is randomly chosen from jar k. Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e. , it is m/(m + n) .

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QUESTION:

Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, then a ball is randomly chosen from jar 2 and transferred to jar 3, etc. Finally, a ball is randomly chosen from jar k. Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e. , it is m/(m + n) .

ANSWER:

Step 1 of 3

Given that,

Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, then a ball is randomly chosen from jar 2 and transferred to jar 3, etc. Finally, a ball is randomly chosen from jar k.

It is required to show that the probability that the last ball is white is the same as the probability that the first ball is white; that is,.

Suppose the events of getting a white and black ball from the jar be , respectively.

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