Suppose you have a 20-sided die with each side labeled with a number from 1 to 5. Here is the breakdown of how many sides have each number labeled: Table describing 20-sided die Number displayed on die How many sides have this number labeled 1 3 2 4 3 7 4 5 5 1 Understanding Sample Space Guiding Discussion Question: What is the sample space associated to this die? How do you know? Do we use repeating occurrences in the sample space, or just list possible outcomes? Practice with Probability Rules Find each of the following probabilities: P(1) P(2) P(3) P(4 or 5) P(even) P(odd or 2) P(even or 2) P(rolling a 1 and a 2 at the same time) P(rolling a 3 and then rolling a 4 afterward) P(rolling an even number and then rolling an odd number) Guiding Discussion Questions: How do you know what probability rule to use to do each computation? Are there events that are independent or disjoint? How does this affect your computations? Can you do these computations in multiple ways, to check your understanding of probability rules? For example, are there any computations that you can use a counting method for, then also use one of the probability rules, and check to see if you get the same answer? Are these probabilities theoretical or empirical? How do you know? Using a Venn Diagram Draw a Venn Diagram using one circle to represent "even numbers" and another circle to represent "1, 2, 3". Include the entire sample space of the die in your diagram. (Not all will be inside the circles.) Guiding Discussion Questions: How are probabilities illustrated by the various parts of the Venn Diagram? Find two parts of the Venn Diagram which are complements of each other. How do you know they are complements?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Data...

Suppose you have a 20-sided die with each side labeled with a number from 1 to 5. Here is the breakdown of how many sides have each number labeled:

Table describing 20-sided die

Number displayed on die	How many sides have this number labeled
1	3
2	4
3	7
4	5
5	1

Understanding Sample Space

Guiding Discussion Question:

What is the sample space associated to this die? How do you know?
Do we use repeating occurrences in the sample space, or just list possible outcomes?

Practice with Probability Rules

Find each of the following probabilities:

P(1)
P(2)
P(3)
P(4 or 5)
P(even)
P(odd or 2)
P(even or 2)
P(rolling a 1 and a 2 at the same time)
P(rolling a 3 and then rolling a 4 afterward)
P(rolling an even number and then rolling an odd number)

Guiding Discussion Questions:

How do you know what probability rule to use to do each computation?
Are there events that are independent or disjoint? How does this affect your computations?
Can you do these computations in multiple ways, to check your understanding of probability rules? For example, are there any computations that you can use a counting method for, then also use one of the probability rules, and check to see if you get the same answer?
Are these probabilities theoretical or empirical? How do you know?

Using a Venn Diagram

Draw a Venn Diagram using one circle to represent "even numbers" and another circle to represent "1, 2, 3". Include the entire sample space of the die in your diagram. (Not all will be inside the circles.)

Guiding Discussion Questions:

How are probabilities illustrated by the various parts of the Venn Diagram?
Find two parts of the Venn Diagram which are complements of each other. How do you know they are complements?

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