Chapter 9.9, Problem 6ES

### 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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# An urn contains 25 red balls and 15 blue balls. Two are chosen at random, one after the other, without replacement. a. Use a tree diagram to help calculate the following probabilities: the probability that both bal1 are red, the probability that the first ball is red and the second is not, the probability that the first ball is not red and the second is red, the probability that neither ball is red. b. What is the probability that the second hail is red? c.What is the probability that at least one of the balls is red?

To determine

To use a tree diagram to calculate that both balls are red, the probability that the first ball is red and the second is not, the probability that the first ball is not red and the second is red, the probability that neither ball is red.

Explanation

Given information:

An urn contains 25 red balls and 15 blue balls. Two are chosen at random one after the other without replacement.

Calculation:

Let R1= first ball is red.

B1= first ball is blue.

R2= second ball is red.

B2= second ball is blue.

Total balls =25+15.

Now calculate the probabilities on first draw

P(R1)=2540P(B1)=1540

Now on the second draw if the red ball is already taken out, number of red balls will be 24 and if blue ball is taken out the number of blue balls will be 14 and the total number of balls 39

To determine

What is the probability that the second ball is red?

To determine

To find the probability that at least one of the balls is red.

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