Chapter 9.9, Problem 13ES

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Chapter
Section

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# One urn contains 10 red balls and 25 green balls, and a second urn contains 22 red balls and 15 green balls. A ball is chosen as follows: First an urn is selected by tossing a loaded coin with probability 0.4 of landing heads up and probability 0.6 of landing tails up. If the coin lands heads up, the first urn is chosen: otherwise, the second urn is chosen. Then a ball is picked at random from the chosen urn. a. What is the probability that the chosen ball is green?

To determine

To find out the probability that chosen ball is green.

Explanation

Given information:

One urn contains 10 red balls and 25 green balls and second urn contains 22 red balls and 15 green balls. The probability of choosing the first urn is 0.4 and the probability of choosing the second urn is 0.6.

Calculation:

Let A= event of choosing the green ball.

E1= event of choosing the blue ball from first bag.

E2= event of choosing the blue ball from second bag.

P(A)=i=1nP(Ei)(A|Ei){using multiplication theorem of probability}

To determine

To find out the probability that chosen ball is green and it came from the first urn.

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