   Chapter 9.1, Problem 16ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. Let BBR denote the outcome where the color appearing face up on the first and second rolls is blue and the color appearing face up on the third roll is red. Because there are as many faces of one color as of any other, the outcomes of this experiment are equally likely. List all 27 possible outcomes. Consider the event that all three rolls produce different colors. One outcome in this event is RBY and another KYB. List all outcomes in the event. What is the probability of the event? Consider the event that two of the colors that appear lace up are the same. One outcome in this event is RRB and another is RBR. List all outcomes in the event. What is the probability of the event?

To determine

(a)

To write:

The sample space of all possible color combination, when we throw a die three times.

Explanation

Given:

We roll a die three times, two faces of die are Red, two are Yellow and two are Blue.

Interpretation:

To determine

(b)

To find:

The list of the all events where the color is different and finds the probability of such event where colors are different.

To determine

(c)

To find:

The list of the all the events that two of the colors that appear face up are the same and find the probability of such event where two of the colors that appear face up are the same.

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