Untitled Lesson

Goal: Find probabilities.

Probability and Odds
6.7

Copyright © Holt McDougal. All rights reserved.

130Chapter 6 • Pre-Algebra Notetaking Guide

Vocabulary

Outcomes:

Event:

Favorable
outcomes:

Probability:

Theoretical
probability:

Experimental
probability:

Odds in
favor:

Odds
against:

The ratio of the number of unfavorable outcomes to
the number of favorable outcomes is called the odds
against an event.

The ratio of the number of favorable outcomes to the
number of unfavorable outcomes is called the odds in
favor of an event.

A probability that is based on repeated trials of an
experiment is called an experimental probability.
Each trial in which the event occurs is a success.

A theoretical probability is based on knowing all of
the equally likely outcomes of an experiment.

The probability that an event occurs is a measure
of the likelihood that the event will occur.

The outcomes for a specified event are called
favorable outcomes.

An event is an outcome or a collection of outcomes.

The possible results of an experiment are outcomes.

LAH_PA_11_FL_NTG_Ch0#6C2CEF.qxd 3/4/09 11:16 PM Page 130

Chapter 6 • Pre-Algebra Notetaking Guide

131

Copyright © Holt McDougal. All rights reserved.

Suppose you roll a number cube. What is the probability that you
roll an odd number?

Solution

Rolls of

are odd, so there are

favorable outcomes.

There are

possible outcomes.

P(

) �

�

�
�1
2�

�3
6�

Number of favorable outcomes
Number of possible outcomes
rolling an odd number

6

3

1, 3, and 5

Example 1

Finding a Probability

Checkpoint

1. Suppose you roll a number cube. What is the probability that you
roll a number less than 5?

�2
3�

2. Suppose you roll a number cube. What is the probability that you
roll a number that is a multiple of 3?

�1
3�

Probability of an Event

The probability of an event when all outcomes are equally likely is:

P(event) �Number of favorable outcomes����
Number of possible outcomes

LAH_PA_11_FL_NTG_Ch0#6C2CEF.qxd 3/4/09 11:17 PM Page 131

Copyright © Holt McDougal. All rights reserved.

132Chapter 6 • Pre-Algebra Notetaking Guide

You plant 32 seeds of a certain flower and 18 of them sprout.
Find the experimental probability that the next flower seed
planted will sprout.

Solution

P(flower seed will sprout) �

�

Simplify.

Answer: The experimental probability that the next flower seed will

sprout is

, or

.

0.5625

�1
9
6�

�1
9
6�

�1
3
8
2�

Example 2

Finding Experimental Probability

Number of successes
Number of trials

Suppose you randomly choose a number between 1 and 16.

a. What are the odds in favor of choosing a prime number?
b. What are the odds against choosing a prime number?

Solution

a. There are

favorable outcomes (

) and

16 �

�

unfavorable outcomes.

Odds in favor �

�

�

The odds are

, or

to

, that you choose a prime number.

b. The odds against choose a prime number are

, or

to

.3

5
�5
3�

5

3
�3
5�

�3
5�

�1
6
0�
Number of favorable outcomes����
Number of unfavorable outcomes

10

6

2, 3, 5, 7, 11, and 13

6

Example 3

Finding the Odds

Experimental Probability

The experimental probability of an event is:

P(event) �Number of successes���
Number of trials

LAH_PA_11_FL_NTG_Ch0#6C2CEF.qxd 3/4/09 11:17 PM Page 132

Chapter 6 • Pre-Algebra Notetaking Guide

133

Copyright © Holt McDougal. All rights reserved.

Goal: Determine whether a game is fair.

Fair Games

Vocabulary

Fair game A game in which all players are equally likely to win

In a game, two players roll a number cube. For each round, player 1
scores a point if the number cube shows a multiple of 2. Player 2
scores a point if the number cube shows a multiple of 3. The player
who scores 8 points first wins. Determine whether the game is fair.

Solution

For player 1, rolls of

are multiples of 2, so there are

favorable outcomes out of

possible outcomes.

P(rolling a multiple of 2)

�

For player 2, rolls of

are

, so there are

favorable outcomes out of

possible outcomes.

P(

)
�

Because the probabilities

the same, the players

equally likely to win the game. Therefore, the game

fair.

is not

are not

are not

�1
3�

�2
6�
rolling a multiple of 3

6

2

multiples of 3

3 and 6

�1
2�

�3
6�

6

3

2, 4, and 6

Example 1

Determining Whether a Game is Fair

Focus On
Probability

Use after Lesson 6.7

LAH_PA_11_FL_NTG_Ch0#6C45BD.qxd 3/5/09 2:12 AM Page 133

Copyright © Holt McDougal. All rights reserved.

134Chapter 6 • Pre-Algebra Notetaking Guide

A bag contains 5 cards, numbered 1–5. In a game, two players
each draw a card from the bag. The player who draws the lesser
number wins. Determine whether the game is fair.

Solution

The total number of ways of winning

equal to the total

number of ways of losing. Each player has a

% chance of

winning, so the game

fair.

is

50

is

Example 2

Determining Whether a Game is Fair

In a game, two players spin the spinner shown once. If the sum of
the spins is even, player 1 wins. If the sum is odd, player 2 wins.
Determine whether the game is fair.

Solution

From the list, you can see that there are

outcomes in which player

1 wins and

outcomes in which player 2 wins. Because there are

outcomes in which player 1 can win, the game

fair.

is not

more

4

5

Example 3

Determining Whether a Game is Fair

Player 1

Player 2

Winner

1

1

Player 1

1

2

1

3

2

1

2

2

2

3

3

1

3

2

3

3

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Number that player

5

4

3

draws

Number of ways

0

1

that player wins

Number of ways

4

that player loses

0

1

2

3

4

3

2

1

2

1

2

3

LAH_PA_11_FL_NTG_Ch0#6C2CEF.qxd 3/4/09 11:28 PM Page 134