pre-algebra 9-1 probability pledge & moment of silence

Pre-Algebra

9-1 Probability

Pledge & Moment of Silence

Pre-Algebra

9-1 Probability

Pre-Algebra HOMEWORK

Page 449 #1-8

&

Page 453 #1-6

Our Learning GoalStudents will be able to find theoretical probabilities, including dependent and independent events; estimate probabilities using experiments and simulations; use The Fundamental Counting Principle, permutations, and combinations; and convert between probability and odds of a specified outcome.

Our Learning Goal Assignments

• Learn to find he probability of an event by using the definition of

probability (9-1)

• Learn to estimate probability using experimental methods (9-2)

Pre-Algebra

9-1 Probability

Student Learning Goal Chart

Pre-Algebra

9-1 Probability

9-1 AND 9-2

FAST TRACK!

Pre-Algebra

9-1 Probability

Today’s Learning Goal Assignment

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

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 occurring0.874

0.351

0.794

9-2 Experimental ProbabilityToday’s Learning Goal Assignment

Learn to estimate probability using experimental methods.

9-2 Experimental Probability

Lesson Quiz: Part 11. Of 425, 234 seniors were enrolled in a math

course. Estimate the probability that a randomly selected senior is enrolled in a math course.

2. Mason made a hit 34 out of his last 125 times at bat. Estimate the probability that he will make a hit his next time at bat.

0.27, or 27%

0.55, or 55%


Lesson Quiz: Part 2

3. Christina polled 176 students about their favorite ice cream flavor. 63 students’ favorite flavor is vanilla and 40 students’ favorite flavor is strawberry. Compare the probability of a student’s liking vanilla to a student’s liking strawberry.

about 36% to about 23%

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


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


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


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


6

Pre-Algebra

9-1 Probability

Try This: Example 1B Continued


6


6


6

Pre-Algebra

9-1 Probability

Try This: Example 1B Continued


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. 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


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


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%


Pre-Algebra

9-1 Probability


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


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


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.


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


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


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


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


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 occurring0.874

0.351

0.794

Pre-Algebra

9-1 Probability9-2 Experimental Probability

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpUse the table to find the probability of each event.

1. A or B occurring

2. C not occurring

3. A, D, or E occurring

0.494

0.742

0.588

Pre-Algebra


Problem of the Day

A spinner has 4 colors: red, blue, yellow, and green. The green and yellow sections are equal in size. If the probability of not spinning red or blue is 40%, what is the probability of spinning green? 20%

Today’s Learning Goal Assignment

Learn to estimate probability using experimental methods.

Vocabulary

experimental probability

In experimental probability, the likelihood of an event is estimated by repeating an experiment many times and observing the number of times the event happens. That number is divided by the total number of trials. The more the experiment is repeated, the more accurate the estimate is likely to be.

number of times the event occurs

total number of trialsprobability

A. The table shows the results of 500 spins of a spinner. Estimate the probability of the spinner landing on 2.

Additional Example 1A: Estimating the Probability of an Event

The probability of landing on 2 is about 0.372, or 37.2%.

probability 500186number of spins that landed on 2

total number of spins =


A. Jeff tosses a quarter 1000 times and finds that it lands heads 523 times. What is the probability that the next toss will land heads? Tails?

P(heads) =

P(heads) + P(tails) = 1 The probabilities must equal 1.

0.523 + P(tails) = 1

P(tails) = 0.477

= 0.5231000523

B. A customs officer at the New York–Canada border noticed that of the 60 cars that he saw, 28 had New York license plates, 21 had Canadian license plates, and 11 had other license plates. Estimate the probability that a car will have Canadian license plates.

= 0.35The probability that a car will have Canadian license plates is about 0.35, or 35%.

Additional Example 1B: Estimating the Probability of an Event

probability number of Canadian license plates 21 total number of license plates 60

=


B. Josie sells TVs. On Monday she sold 13 plasma displays and 37 tube TVs. What is the probability that the first TV sold on Tuesday will be a plasma display? A tube TV?

P(plasma) = 0.26

P(plasma) + P(tube) = 1

0.26 + P(tube) = 1

P(tube) = 0.74

probability ≈ 1350

number of plasma displays total number of TVs

=13 + 37

13 =

Use the table to compare the probability that the Huskies will win their next game with the probability that the Knights will win their next game.

Additional Example 2: Application


The Knights are more likely to win their next game than the Huskies.

number of winstotal number of games

probability

probability for a Huskies win 13879 0.572

146probability for a Knights win 90 0.616

Use the table to compare the probability that the Huskies will win their next game with the probability that the Cougars will win their next game.

Try This: Example 2


The Huskies are more likely to win their next game than the Cougars.

number of winstotal number of games

probability

probability for a Huskies win 13879 0.572

150probability for a Cougars win 85 0.567

Lesson Quiz: Part 1

1. Of 425, 234 seniors were enrolled in a math course. Estimate the probability that a randomly selected senior is enrolled in a math course.

2. Mason made a hit 34 out of his last 125 times at bat. Estimate the probability that he will make a hit his next time at bat.

0.27, or 27%

0.55, or 55%

Lesson Quiz: Part 2

3. Christina polled 176 students about their favorite ice cream flavor. 63 students’ favorite flavor is vanilla and 40 students’ favorite flavor is strawberry. Compare the probability of a student’s liking vanilla to a student’s liking strawberry.

about 36% to about 23%

pre-algebra 9-1 probability pledge & moment of silence

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