3. Three balls are divided between two containers. During each period a ball is randomly chosen and switched to other container. a) Find (in steady state) the fraction of the time that a container will contain 0,1,2,3 balls. b) If container 1 contains no balls, on average how many periods will go by before it again contains no balls. c) If container 1 contains balls, on average how many periods will go by before it contains 3 balls.

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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3. Three balls are divided between two containers.
During each period a ball is randomly chosen and
switched to other container.
a) Find (in steady state) the fraction of the time that a
container will contain 0,1,2,3 balls.
b) If container 1 contains no balls, on average how
many periods will go by before it again contains no
balls.
c) If container 1 contains balls, on average how many
periods will go by before it contains 3 balls.
Transcribed Image Text:3. Three balls are divided between two containers. During each period a ball is randomly chosen and switched to other container. a) Find (in steady state) the fraction of the time that a container will contain 0,1,2,3 balls. b) If container 1 contains no balls, on average how many periods will go by before it again contains no balls. c) If container 1 contains balls, on average how many periods will go by before it contains 3 balls.
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