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Statistics / Introduction to Probability, 2 / Chapter 1 / Problem 23

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

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QUESTION:

We have two jars, each initially containing an equal number of balls. We perform four successive ball exchanges. In each exchange, we pick simultaneously and at random a ball from each jar and move it to the other jar. What is the probability that at the end of the four exchanges all the balls will be in the jar where they started?

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QUESTION:

We have two jars, each initially containing an equal number of balls. We perform four successive ball exchanges. In each exchange, we pick simultaneously and at random a ball from each jar and move it to the other jar. What is the probability that at the end of the four exchanges all the balls will be in the jar where they started?

ANSWER:

Step 1 of 2

Given that,

We have two jars, each initially containing an equal number of balls. We perform four successive ball exchanges. In each exchange, we pick simultaneously and at random a ball from each jar and move it to the other jar.

Suppose the probability that after k exchanges, a jar will contain number of balls that started in the jar and balls that started in the other jar be .

It is required to compute the probability that at the end of the four exchanges all the balls will be in the jar where they started; that is, .

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