×
Log in to StudySoup
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 1.3 - Problem 16e
Join StudySoup for FREE
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 1.3 - Problem 16e

Already have an account? Login here
×
Reset your password

# Bowl A contains three red and two white chips, and bowl B ISBN: 9780321923271 41

## Solution for problem 16E Chapter 1.3

Probability and Statistical Inference | 9th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Probability and Statistical Inference | 9th Edition

4 5 1 304 Reviews
29
5
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

Step 3 of 3

##### ISBN: 9780321923271

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

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