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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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Urn I contains 2 white and 4 red balls, whereas urn II

Chapter 3, Problem 23P

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QUESTION:

Problem 23P

Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen from urn I and put into urn II, and a ball is then randomly selected from urn II. What is

(a) the probability that the ball selected from urn IIis white?

(b) the conditional probability that the transferred ball was white given that a white ball is selected from urn II?

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QUESTION:

Problem 23P

Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen from urn I and put into urn II, and a ball is then randomly selected from urn II. What is

(a) the probability that the ball selected from urn IIis white?

(b) the conditional probability that the transferred ball was white given that a white ball is selected from urn II?

ANSWER:

Step 1 of 3

A bag contain a white and black balls. Balls are chosen from the bag according to the following method.

(1) A ball is chosen at random and is discarded.

(2) 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.

Let denote the probability that the last ball in the bag is white.

We have to prove that = .

 

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