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23 A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: A. A ball is chosen at random and is discarded. B. A second ball is then chosen. If its color is different from that of the preceding ball, it is replaced in the bag and the process is repeated from the beginning. If its color is the same, it is discarded and we start from step 2.

23 A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: A. A ball is chosen at random and is discarded. B. A second ball is then chosen. If its color is different from that of the preceding ball, it is replaced in the bag and the process is repeated from the beginning. If its color is the same, it is discarded and we start from step 2.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section: Chapter Questions
Problem 3PTTS
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23 A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: A. A ball is chosen at random and is discarded. B. A second ball is then chosen. If its color is different from that of the preceding ball, it is replaced in the bag and the process is repeated from the beginning. If its color is the same, it is discarded and we start from step 2. In other words, balls are sampled and discarded until a change in color occurs, at which point the last ball is returned to the urn and the process starts anew. Let Pa,b denote the probability that the last ball in the bag is white. Prove that Hint: Use induction on k = a + b. Pa,b - 1 2
Transcribed Image Text:23 A bag contains a white and b black balls. Balls are chosen from the bag according to the following method: A. A ball is chosen at random and is discarded. B. A second ball is then chosen. If its color is different from that of the preceding ball, it is replaced in the bag and the process is repeated from the beginning. If its color is the same, it is discarded and we start from step 2. In other words, balls are sampled and discarded until a change in color occurs, at which point the last ball is returned to the urn and the process starts anew. Let Pa,b denote the probability that the last ball in the bag is white. Prove that Hint: Use induction on k = a + b. Pa,b - 1 2
Expert Solution
Step 1: Given information

The provided information  is as follows:

The  P subscript straight a comma straight b end subscript denotes the probability that the last ball in the bag is white.

The white ball is the a and the black ball is the b.


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I have a question about Step 4. I cannot figure out why

P(E a,b| WcBc) = P(Ei, j). My guess is that it is because of the inductive hypothesis. However, I don't know why: I don't know what P(Ei,j) means and I don't what P(E a,b| WcBc) represents.

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