What is the probability that the spinner will land on blue?

In this lesson you will learn how to calculate the probability of an event by creating a ratio.

Let’s Review

Ratios can be used to represent fractions of an area or of a set.

A Common Mistake

Every event must have an equal probability of occurring.

Core Lesson

Probability is the likelihood that an event will take place.

Core Lesson

What is the probability that the spinner will land on blue?

12 3

45

678

Core Lesson

Samuel has a bowl of fruit containing 3 apples, 2 oranges and 5 pears. If he

randomly picks 1 piece of fruit from the bowl, what is the probability it will be a

pear or an apple?

Core Lesson

apples32 oranges5 pears+

10 fruits total

In this lesson you have learned how to calculate the probability of an event by creating a ratio.

Guided Practice

When you roll a number cube with faces numbered 1, 2, 3, 4, 5, 6, what is the probability it will land on an odd number?

Quick Quiz

A bag has 40 blue chips and 60 green chips. What is the probability that you will randomly pick a blue chip from the bag?A bag has 4 blue marbles, 5 red marbles and 6 green marbles. What is the probability of picking a red or blue marble?

1

2

Lesson 2

In this lesson you will learn how to describe the probability of an event by using a number

line.

Core Lesson

The probability continuum:

l limpossible certain

Core Lesson

The probability continuum:

l limpossible certain

0 1

Core Lesson

The probability continuum:

l l0 1

l

equally likely

l l

unlikely likelyimpossible certain

Core Lesson

Core Lesson

The probability continuum:

l l0 1

l

equally likely

l l

unlikely likelyimpossible certain

Core Lesson

Core Lesson

The probability continuum:

l l0 1

l

equally likely

l l

unlikely likelyimpossible certain

In this lesson you have learned how to describe the probability of an event by using a number

line.

Guided Practice

There are 12 pairs of socks in Flora’s drawer, 9 are red, 2 are blue and 1 is green. She takes out one pair of socks without looking at the color. Describe (in words) the likelihood of Flora picking out a pair of red socks.

Extension Activities

A container contains 2 blue, 1 green, and 4 orange and 5 yellow marbles. Find the probability of picking each marble and then put the probabilities in order from unlikely to likely chance of occurring.

Lesson 3

How can you use the theoretical probability to

predict the results from an experiment?

If you were to roll a six-sided die 600 times how many times would you

predict you would roll a 3 or 6?

In this lesson you will learn how to predict the frequency of

an event by using the theoretical probability.

Core Lesson

If you were to roll a six-sided die 600 times how many times would you

predict you would roll a 3 or 6?

Core Lesson

If you were to roll a six-sided die 600 times how many times would you

predict you would roll a 3 or 6?

In this lesson you have learned how to predict the frequency of

an event by using the theoretical probability.

Guided Practice

If you were to spin 400 times, predict how many times you would land on blue?

Quick Quiz

A bag has 4 blue marbles, 6 green and 2 red. Marcus will pick a marble from the bag and return it 60 times. Of the 60 times predict how many times you would expect Marcus to pick a blue marble?

Quick Quiz

If you were to roll a six-sided die 150 times. How many times would you expect to roll a number greater than 4?

Lesson 4

Trial Sum1 52 33 74 95 7

Trial Sum6 87 68 79 5

10 9

How do you find the experimental probability of rolling a 7 based off the

table below?

In this lesson you will learn how to interpret a set of data by comparing experimental and theoretical probability.

Let’s Review

Experimental Probability:

Core Lesson

Trial Sum1 52 33 74 95 7

Trial Sum6 87 68 79 5

10 9

Number of times a 7 was rolled:

1

Trial Sum6 87 68 79 5

10 9

23

Core Lesson

1+1 1+2 1+3 1+4 1+5 1+62+13+14+15+16+1

2+2 2+3 2+4 2+5 2+63+24+25+26+2

3+3 3+4 3+5 3+64+3 4+4 4+5 4+65+3 5+4 5+5 5+66+3 6+4 6+5 6+6

2 3 4 5 6 77

77

77

3 445

55

66

66

88

88

8

99

99

1010

10

111112

In this lesson you have learned how to interpret a set of data by comparing experimental and theoretical probability.

Guided Practice

Results from rolling a six-sided die:Rolled # of

times1 62 153 184 115 36 7

What is the experimental probability of rolling a 4? How does that compare to the theoretical probability?

Quick Quiz

After 60 spins, Chris had the following results:

A

AA

B

BB

CC

Letter #A 29B 16C 15

What is the experimental probability of spinning a “B”? How does that compare to the theoretical probability?

Quick QuizIn a survey, Scott asked 50 people if they voted for the current mayor. He recorded the results in this table:

Based on the survey, what is the probability that the next person will say “No”?A. 5% B. 20% C. 40% D. 67%

Yes No Private22 20 3

Lesson 5

Score! Miss!

Scored Missed1 1

Score!

220 5

How do you find the experimental probability of him making his next throw?

In this lesson you will learn how to find the experimental

probability by creating a ratio.

Let’s Review

Core Lesson

Theoretical Probability:

Core Lesson

Experimental Probability:

3 times10 trials

Core Lesson

Scored Missed20 5

In this lesson you have learned how to find the experimental

probability by creating a ratio.

Guided Practice

After 50 spins, Chris landed on green 22 times. What is the experimental probability of landing on green? How does it compare to the theoretical probability?

Quick Quiz

A company manufactures CD players. The quality control department checks 600 CD players and discovers that 12 of them are defective. What is the probability that a CD player is not defective?

Quick Quiz

The ticket salesperson at the fair noticed that 12 of the first 40 people buying tickets paid with a credit card. What is the experimental probability that the next customer to buy a ticket will pay with a credit card?

How can you use survey results to make predictions

for a whole population?

For example, in a school of 300, Chris surveyed 80 students and found that

44 students prefer chocolate ice cream.

Lesson 6

In this lesson you will learn how to predict the frequency of an event by using the results

from experiments.

Core Lesson

In a school of 300, Chris surveyed 80 students and found that 44 students

prefer chocolate ice cream.

Core Lesson

Core Lesson

According to the survey results, we can predict that 165 students at Chris’ school

prefer chocolate ice cream.

Core Lesson

To predict frequencies of an event using the experimental probability:

In this lesson you have learned how to predict the frequency of an event by using the results

from experiments.

Guided PracticeKaren spun a spinner 50 times and recorded her results in the table below. The spinner had five numbered sections.

Section Frequency

1 132 23 104 125 7

Based on the results in the table, how many times should Karen expect the spinner to land on section 3 or 4 if she spins the spinner 300 times?

Extension Activities

Have students do an experiment in which they roll a die 25 times. Then have them use their experimental probabilities to find how many times they would expect a 1, 2, 3, etc.. If they were to roll 100 or 1,000 more times.

Quick QuizThe mayor of a town conducted an opinion survey of 90 randomly selected voters. The mayor wants to determine if a new shopping mall should be built in town. The survey results are shown below.

Want a new mall 60

Do Not Want a New Mall

20

No Opinion 10

There are 1,440 voters in town. How many voters would be expected to want the new shopping mall built?

Quick QuizThe spinner below is spun 20 times. The table shows the results.

Based on these results, how many times would 2 be expected to appear in 60 spins?

Section Frequency1 52 83 24 5

Lesson 7

How do you determine the sample space for rolling a

six-sided die?

In this lesson you will learn how to analyze the probability of an event by assigning equal

probability to all outcomes.

Core Lesson

Sample space: set of all possible outcomes in an experiment.

Core Lesson

{1, 2, 3, 4, 5, 6}

+ + + + + = 1

P(4)=

Core Lesson

+ =1What about me?+ + + + + + +

=1

In this lesson you have learned how to analyze the probability of an event by assigning equal

probability to all outcomes.

Guided Practice

Using the spinner below, what is the sample space? What is the probability that the spinner will land on “B” as a percentage?

A B

CD

E

Quick Quiz

Mr. Smith’s class has 12 boys and 12 girls. Mr. Smith will pick someone at random to take attendance. What is the probability that Jane, a girl, will be selected? What is the probability of a girl?

Quick Quiz

A bag has only four marbles in it. One blue, one green, one red and one yellow. What is the sample space? What is the probability of selecting a green marble?

How do you find the probability of pulling a blue

marble?A bag is full of 3 blue, 4 green and 2

red marbles.

In this lesson you will learn to find the probability of events with multiple possibilities by combining their probabilities.

Let’s Review

Theoretical Probability:

12 3

45

678

A Common Mistake

Sample space:

A B

CA

C

{A, B, C}

{A, A, B, C, C}

Core Lesson

+ + + + + + + + = 1

1 2 3 4 5 6 7 8 9

Core Lesson

{1, 2, 3, 4, 5, 6}

+ + + + + = 1

What is the probability of rolling a 4 or greater?

P(≥4)=

In this lesson you have learned how to find the probability of

events with multiple possibilities by combining their

probabilities.

Guided Practice

You roll a six-sided die. What is the probability of rolling an odd number?

Quick Quiz

You roll a six-sided die. What is the probability of rolling a 3 or greater?

Quick Quiz

What is the probability of spinning a 3 or higher on the spinner below?

1 234

42

1 3

Lesson 8

How do you describe the discrepancies in

experimental and theoretical probabilities ?

After 6 trials, Chris found that the experimental probability for rolling a 4

was .

In this lesson you will learn how to explain discrepancies in

results from a probability model by comparing

experimental and theoretical probabilities.

Core Lesson

After 6 trials, Chris found that the experimental probability for rolling a 4

was .

Core Lesson

Theoretical:

Experimental: 6 trials20 trials50 trials

Core Lesson

Sample space is too large.

In this lesson you have learned how to explain discrepancies in results from probability models

by comparing experimental and theoretical probabilities.

Guided PracticeCompare the theoretical and experimental probabilities of the spinner landing on green. Are there any discrepancies? Why or why not?

Section FrequencyGreen 5

Orange 9Red 3

Yellow 7Blue 6

Quick Quiz

A bag has 4 blue marbles, 6 green marbles and 10 red marbles. A marble is picked at random and then returned. After 50 pulls, 35 red marbles were chosen. Is there a discrepancy between the experimental and theoretical probabilities? Why or why not?

Quick Quiz

The table below shows the results from 20 tosses of a fair coin.

Heads Tails11 9

Is there a discrepancy in the theoretical and experimental probabilities of getting a tails? Why or why not?