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An urn initially contains 1 red and 1 blue ball. At each
Chapter 3, Problem 27STE(choose chapter or problem)
Problem 27STE
An urn initially contains 1 red and 1 blue ball. At each stage, a ball is randomly withdrawn and replaced by two other balls of the same color. (For instance, if the red ball is initially chosen, then there would be 2 red and 1 blue balls in the urn when the next selection occurs.) Show by mathematical induction that the probability that there are exactly i red balls in the urn after nstages have been completed is .
Questions & Answers
QUESTION:
Problem 27STE
An urn initially contains 1 red and 1 blue ball. At each stage, a ball is randomly withdrawn and replaced by two other balls of the same color. (For instance, if the red ball is initially chosen, then there would be 2 red and 1 blue balls in the urn when the next selection occurs.) Show by mathematical induction that the probability that there are exactly i red balls in the urn after nstages have been completed is .
ANSWER:
Step 1 of 2
An urn contains 1 red and 1 blue ball. At each stage, a ball is randomly withdrawn and replaced by two other balls of the same color.
By using the mathematical induction we have to show that the probability that there are exactly i red balls in the urn after n stages have been completed is , 1
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