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Bowl A contains three red and two white chips, and bowl B

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 16E Chapter 1.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 16E

PROBLEM 16E

Bowl A contains three red and two white chips, and bowl B contains four red and three white chips. A chip is drawn at random from bowl A and transferred to bowl B. Compute the probability of then drawing a red chip from bowl B.

Step-by-Step Solution:

Solution:

Step 1 of 3 :

Here bowl A contains 3 red and 2 white chips bowl B contains 4 red and three white chips . If  chip is drawn at random from bowl A and transferred to bowl B.  we have to Compute the probability of  drawing a red chip from bowl B.


Step  2 of 3:

It is given that                          

Bowl A                                   Bowl B

No of red chips = 3              No of red chips= 4                

No of white chips = 2          No of white chips = 3

It is also given that a chip is drawn randomly from bowl A and transferred to bowl B.

So then  there will be two chances that  drawing a red chip from Bowl B.

  1. Drawing a white chip from bowl A and transferred to bowl B and then drawing a red chip from bowl B.
  2.  Drawing a red chip from bowl A and transferred to bowl B and then drawing a red chip from bowl B.

By bayes theorem probability of drawing a red chip from bowl B will be the addition of these two probabilities.

Let define the events

A = drawing a red chip from Bowl B after transferring a chip from bowl A to B which is randomly chosen.

W=  a white chip transferred from bowl A to B.

R =  a red chip transferred from bowl A to B.

So

P(R)= 3/5

P(W) = 2/5

P(A) = P(W)  P(A/W) +P(R)P(A/R)

P(A/W)= P(that a red chip is drawn from bowl B given that a white bowl is transferred from A to B .

            =  4/8

P(A/R) = P(that a red chip is drawn from bowl B given that a red bowl is transferred from A to B

            = 5/8

So the probability that  a red chip is drawn from bowl B given that a red bowl is transferred from A to B is 5/8.


Step 3  of 3:

 

Then

Probability of  drawing a red chip from bowl B

P(A) =  (⅗  5/8) + (2/5 4/8)

     =  15/40 + 8/40  

        = 23/40

        = 0.575

So the probability that  drawing a red chip from bowl B is 0.57.


Step 2 of 3

Chapter 1.3, Problem 16E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Bowl A contains three red and two white chips, and bowl B