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How can 20 balls, 10 white and 10 black, be put into two

Chapter 3, Problem 3STE

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QUESTION:

Problem 3STE

How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it?

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QUESTION:

Problem 3STE

How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it?

ANSWER:

Step 1 of 2

(a)

We are asked to find the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it.

Let the  balls be divided into 2 urns in the following way.

Let urn 1 contains  black and   white and urn 2 contains  black and  white.

The probability of drawing a white ball from urn 1 is,

 The probability of drawing a white ball from urn 2 is,

 

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