Pre-Algebra

9-1 Probability9-1 Probability

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

9-1 Probability

Warm UpWrite each fraction in simplest form.

1. 2.

3. 4.

Pre-Algebra

9-1 Probability

1620

1236

864

39195

4

5

1

3

1

8

1

5

Pre-Algebra

9-1 Probability

Problem of the Day

A careless reader mixed up some encyclopedia volumes on a library shelf. The Q volume is to the right of the X volume, and the C is between the X and D volumes. The Q is to the left of the G. X is to the right of C. From right to left, in what order are the volumes?D, C, X, Q, G

Pre-Algebra

9-1 Probability

Learn to find the probability of an event by using the definition of probability.

Pre-Algebra

9-1 Probability

Vocabulary

experimenttrialoutcomesample spaceeventprobabilityimpossiblecertain

Pre-Algebra

9-1 Probability

An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.

Experiment Sample Space

flipping a coin heads, tails

rolling a number cube 1, 2, 3, 4, 5, 6

guessing the number of whole numbers jelly beans in a jar

Pre-Algebra

9-1 Probability

An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.

• A probability of 0 means the event is impossible, or can never happen.

• A probability of 1 means the event is certain, or has to happen.

• The probabilities of all the outcomes in the sample space add up to 1.

Pre-Algebra

9-1 Probability

0 0.25 0.5 0.75 1

0% 25% 50% 75% 100%

Never Happens about Alwayshappens half the time happens

14

12

340 1

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Additional Example 1A: Finding Probabilities of Outcomes in a Sample Space

A. The basketball team has a 70% chance of winning.

The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%.

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Additional Example 1B: Finding Probabilities of Outcomes in a Sample Space

B.

Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is

P(1) = .38

Pre-Algebra

9-1 Probability

Additional Example 1B Continued

Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = .3

8

Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = = .2

814

Check The probabilities of all the outcomes must add to 1.

38

38

28

++ = 1

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Try This: Example 1A

A. The polo team has a 50% chance of winning.

The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%.

Pre-Algebra

9-1 Probability

Give the probability for each outcome.

Try This: Example 1B

B. Rolling a number cube.

One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) = . 1

6

Outcome 1 2 3 4 5 6

Probability

One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 1 is P(2) = . 1

6

Pre-Algebra

9-1 Probability

Try This: Example 1B Continued

One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 1 is P(3) = . 1

6

One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 1 is P(4) = . 1

6

One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 1 is P(5) = . 1

6

Pre-Algebra

9-1 Probability

Try This: Example 1B Continued

One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 1 is P(6) = . 1

6

Check The probabilities of all the outcomes must add to 1.

16

16

16

++ = 116

+16

+16

+

Pre-Algebra

9-1 Probability

To find the probability of an event, add the probabilities of all the outcomes included in the event.

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

Additional Example 2A: Finding Probabilities of Events

A. What is the probability of not guessing 3 or more correct?

The event “not three or more correct” consists of the outcomes 0, 1, and 2.

P(not 3 or more) = 0.031 + 0.156 + 0.313 = 0.5, or 50%.

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

B. What is the probability of guessing between 2 and 5?

The event “between 2 and 5” consists of the outcomes 3 and 4.

P(between 2 and 5) = 0.313 + 0.156 = 0.469, or 46.9%

Additional Example 2B: Finding Probabilities of Events

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

C. What is the probability of guessing an even number of questions correctly (not counting zero)?The event “even number correct” consists of the outcomes 2 and 4.

P(even number correct) = 0.313 + 0.156 = 0.469, or 46.9%

Additional Example 2C: Finding Probabilities of Events

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

Try This: Example 2A

A. What is the probability of guessing 3 or more correct?

The event “three or more correct” consists of the outcomes 3, 4, and 5.

P(3 or more) = 0.313 + 0.156 + 0.031 = 0.5, or 50%.

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

B. What is the probability of guessing fewer than 3 correct?

The event “fewer than 3” consists of the outcomes 0, 1, and 2.

P(fewer than 3) = 0.031 + 0.156 + 0.313 = 0.5, or 50%

Try This: Example 2B

Pre-Algebra

9-1 Probability

A quiz contains 5 true or false questions. Suppose you guess randomly on every question. The table below gives the probability of each score.

C. What is the probability of passing the quiz (getting 4 or 5 correct) by guessing?

The event “passing the quiz” consists of the outcomes 4 and 5.

P(passing the quiz) = 0.156 + 0.031 = 0.187, or 18.7%

Try This: Example 2C

Pre-Algebra

9-1 Probability

Additional Example 3: Problem Solving Application

Six students are in a race. Ken’s probability of winning is 0.2. Lee is twice as likely to win as Ken. Roy is as likely to win as Lee. Tracy, James, and Kadeem all have the same chance of winning. Create a table of probabilities for the sample space.

14

Pre-Algebra

9-1 Probability

Additional Example 3 Continued

11 Understand the Problem

The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.

List the important information:

• P(Ken) = 0.2

• P(Lee) = 2 P(Ken) = 2 0.2 = 0.4

• P(Tracy) = P(James) = P(Kadeem)

• P(Roy) = P(Lee) = 0.4 = 0.1 14

14

Pre-Algebra

9-1 Probability

Additional Example 3 Continued

22 Make a Plan

You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Tracy, James, and Kadeem.

P(Ken) + P(Lee) + P(Roy) + P(Tracy) + P(James) + P(Kadeem) = 1

0.2 + 0.4 + 0.1 + p + p + p = 1

0.7 + 3p = 1

Pre-Algebra

9-1 Probability

Solve33

0.7 + 3p = 1

–0.7 –0.7 Subtract 0.7 from both sides.

3p = 0.3

3p3

0.33

= Divide both sides by 3.

Additional Example 3 Continued

p = 0.1

Pre-Algebra

9-1 Probability

Look Back44

Check that the probabilities add to 1.

0.2 + 0.4 + 0.1 + 0.1 + 0.1 + 0.1 = 1

Additional Example 3 Continued

Pre-Algebra

9-1 Probability

Four students are in the Spelling Bee. Fred’s probability of winning is 0.6. Willa’s chances are one-third of Fred’s. Betty’s and Barrie’s chances are the same. Create a table of probabilities for the sample space.

Try This: Example 3

Pre-Algebra

9-1 Probability

Try This: Example 3 Continued

11 Understand the Problem

The answer will be a table of probabilities. Each probability will be a number from 0 to 1. The probabilities of all outcomes add to 1.

List the important information:

• P(Fred) = 0.6

• P(Betty) = P(Barrie)

• P(Willa) = P(Fred) = 0.6 = 0.213

13

Pre-Algebra

9-1 Probability

Try This: Example 3 Continued

22 Make a Plan

You know the probabilities add to 1, so use the strategy write an equation. Let p represent the probability for Betty and Barrie.

P(Fred) + P(Willa) + P(Betty) + P(Barrie) = 1

0.6 + 0.2 + p + p = 1

0.8 + 2p = 1

Pre-Algebra

9-1 Probability

Solve33

0.8 + 2p = 1

–0.8 –0.8 Subtract 0.8 from both sides.

2p = 0.2

Try This: Example 3 Continued

Outcome Fred Willa Betty Barrie

Probability 0.6 0.2 0.1 0.1

p = 0.1

Pre-Algebra

9-1 Probability

Look Back44

Check that the probabilities add to 1.

0.6 + 0.2 + 0.1 + 0.1 = 1

Try This: Example 3 Continued

Pre-Algebra

9-1 Probability

Lesson QuizUse the table to find the probability of each event.

1. 1 or 2 occurring

2. 3 not occurring

3. 2, 3, or 4 occurring