Unit 11 Cycle 1 Probability - · PDF fileUnit 11 Cycle 1 – Probability Lesson 11.1.3 ... Lesson 11.2.1 – Probability of Independent Compound Events

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Unit 11 Cycle 1 – Probability

Lesson 11.1.1 – Understanding Probability

Vocabulary

Probability Outcome Complement of an event

Active Instruction

ta(1) What is the probability of selecting a blue marble from the bag?

ta(2) What is the probability of selecting a marble that is not blue?

th(1) You put the names of all the students in your class today in a hat. a) What is the total number of favorable outcomes for selecting a girl's name? b) What is the probability of selecting a girl's name? c) What is the probability of not selecting a girl's name? d) What is the probability of selecting a name?

Team Mastery

(3) There are 22 mint candies and 14 chocolate candies in a bag.

b) What is the probability of selecting a chocolate candy?

Lesson Quick Look

Team Name

Team

Complete?

Team Did Not Agree On

Questions…

Write the vocabulary introduced in this lesson:

Today we found the probability of different events. Here’s an example!

Probability = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑒𝑣𝑒𝑛𝑡𝑠

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

The probability of spinning an A or D is 3

5.

This is because: There are 3 favorable outcomes: A, A, D. There are 5 possible outcomes: A, A, B, C, D. The probability of spinning a letter is 1.

This is a certain event because 5

5 = 1.

The probability of spinning a number is 0.

This is an impossible event because 0

5 = 0.

The probability spinning an A is 2

5.

The probability of not spinning an A is 3

5.

Finding the probability of NOT spinning an A, is finding the probability of the complement of the event of spinning an A.

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Lesson 11.1.1 - Homework

1) Diego has a bag containing 13 baseball cards for New York Yankee ball players and 8 baseball cards for Detroit Tigers ball players.

a. What is the total number of outcomes for picking a card out of the bag? b. What is the probability of picking a baseball card for a Detroit Tiger player from the bag? c. What is the probability of not picking a Detroit Tiger baseball card from the bag? d. What is the probability of picking a baseball card for a New York Yankee player from the bag?

2) You have a number cube numbered 1–6.

a. List the favorable outcomes for rolling an odd number. b. What is the probability of rolling an odd number? c. What is the probability of not rolling an odd number? d. What is the probability of rolling a 6?

3) Rita has a bag containing 8 gumdrops, 5 spearmint drops, and 6 chocolate drops.

a) What is the total number of outcomes for selecting a candy? b) What is the probability of picking a chocolate drop? c) What is the probability of not picking a chocolate drop? d) What is the probability of picking a

gumdrop?

Mixed Practice

4) Gina’s lunch bill was $12.50. She left an 18% tip. How much did she pay in all?

5) Divide.

–43 ÷ 5

6) What value of n will make this a proportion? 4

14=

𝑛

35

7) Find the surface area.

8) Your friend has a number cube numbered 1–6. Is the probability of rolling a 3 the same as the probability of rolling a 6? Explain your thinking.

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Lesson 11.1.2 – Decimal and Percent Probability

Active Instruction

ta(1) Write the probability of spinning the spinner as a decimal and percent.

P(red or blue) P(not yellow

ta(2) Estimate the probability of spinning the spinner as a decimal and percent.

P(green)

th(1) A dart is thrown randomly at this board. Estimate the probability of throwing each as a decimal.

a. P(Y) b. P(X or Y) c. P(not X)

Team Mastery

(4) In the skyscraper, Deborah has a 5

36 chance

of selecting a floor that has a restaurant on it. Write her chances of selecting a floor with a restaurant as a percent.

Lesson Quick Look

Team Name

Team

Complete?


Questions…


Today we wrote the probability of events as decimals and percents. Here’s an example! You have a fair octahedron numbered 1–8. Find P(2) when you roll the octahedron once. P(2) means the probability of 2.

So P(2) = 1

8 = 0.125 = 12.5%

We can also estimate the probability! Find P(A) when you spin the spinner once.

Section A takes up about 1

4 of the spinner. So spinning

an A has a probability of about 1

4 , which equals 0.25

or 25%.

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1) Estimate each probability of spinning the spinner

as a percent.

a. P(E)

b. P(B or D)

c. P(not A)

2) Jessica has 16

3 chance of winning a prize in the art

contest. Write her chances of winning a prize as a

decimal.

3) You have an octahedron numbered 1–8. Write the

probability of rolling each as a decimal.

a. P(5 or 6) =

b. P(8) =

c. P(not 6) =

4) There is a 30

11chance of rain today. Write the

probability as a percent.

5) You have a bag that contains tiles with the letters:

A, B, C, D, E, F, G, H, J, and K. Write the probability

of pulling each as a percent.

a. P(J) =

b. P(A, B, or C) =

c. P(not K) =

Mixed Practice

6) Solve.

g – 32 > 44

7) Find the volume.

8) You have a fair number cube numbered 1–6. List

the favorable outcomes of rolling an even number.

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Lesson 11.1.3 – Describing Probability

Active Instruction

ta(1) Describe the likelihood of each event.

P(2) P(odd) P(less than 5)

th(1) a) Write a percent to represent the probability of the spinner landing on an even number. b) Describe the probability of this event.

Team Mastery

(3) A number cube has the following numbers on it:

1, 4, 6, 12, 15, 20 Which event is less likely, P(even) or P(less than 10)?

Lesson Quick Look

Team Name Team Complete?


Questions…


Today we described the probability of an event. Here is an example! If you have a number cube numbered 1–6, then the following probabilities are:

P(1) = 1

6 P(even) =

1

2 P(greater than 2) =

2

3

Now, let’s compare these probabilities on a number line.

The closer a probability is to 1, the more likely it is to occur. That means out of the three events described above, you are most likely to roll a number greater than 2!

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1) You have a bag with 2 red marbles, 10 blue

marbles, and 1 white marble.

a. Describe an event that is impossible to happen.

b. Write a percent to represent the probability of

the event you described. Explain your thinking.

2)

Which event is more likely, P(A) or P(B)?

3) 3) Due to the bus drivers’ strike, there is an 80%

chance that Amanda will be late for school today.

Describe the likelihood that Amanda will be late as

impossible, unlikely, equally likely, likely, or

certain. Explain your thinking.

4) You have an octahedron with sides numbered

1–8.

a. Write the P(even) as a fraction.

b. Describe the likelihood of rolling an even

number as: impossible, unlikely, equally likely,

likely, or certain. Explain your thinking.

Mixed Practice

5) There are 3 cherry popsicles, 1 lime popsicle, and

2 orange popsicles in a box. List the favorable

outcomes for selecting an orange popsicle

randomly from the box.

6) Ms. Neww has some scented erasers in a basket.

1

5 smell like strawberry,

2

5 smell like grape,

1

5 smell

like vanilla, and 1

5 smell like bubble gum. If she

pulls out one eraser, which scent is she most

likely to pull out? Is this event impossible, unlikely,

equally likely, likely, or certain? Explain your

thinking.

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Lesson 11.2.1 – Probability of Independent Compound Events

Vocabulary

Simple event Compound event Sample space Tree diagram Counting principle Probability model

Active Instruction

ta(1) Find the sample space for tossing the

coin and spinning the spinner.

ta(2) Create a probability model for tossing

the coin and spinning the spinner.

th(1) Rob is rolling a number cube numbered

1-6, spinning a spinner, and flipping a coin.

a) How many possibilities are there for rolling the number cube, spinning the spinner, and flipping the coin?

b) Find the probability of rolling a 3, spinning blue, and landing on heads.

c) Find the probability: P(>4 and color and tails)

Team Mastery

(2) Juanita wants to pick an outfit for school. She has three shirts: red, white, and polka-dotted. She has three bottoms: jeans, shorts, and a skirt. a) Create a probability model for randomly selecting an outfit.

Lesson Quick Look



Questions…


Today we found the probability of compound events. Here’s an example! Meg is decorating her living room. Her curtains will either have stripes, zigzags, or dots, and her sofa will either be red, cream, or brown.

We can use a tree diagram to find all the possibilities.

We can also use the counting principle to find the total number of outcomes.

Curtains Sofas Outcomes 3 • 3 = 9

We can also develop a probability model for this event by writing the sample space and the probability of each outcome. S = {SR, SC, SB, ZR, ZC, ZB, DR, DC, DB}

P(S and R) = 1

9 P(S and C) =

1

9 P(S and B) =

1

9

P(Z and R) = 1

9 P(Z and C) =

1

9 P(Z and B) =

1

9

P(D and R) = 1

9 P(D and C) =

1

9 P(D and B) =

1

9

We can use these methods to find the total number of outcomes. Knowing all the outcomes will help us to find the probability of specific events.

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1) You are flipping a coin and rolling a number cube

numbered 1-6.

a. Create a probability model for both flipping the

coin and rolling the number cube.

b. What is the probability that you roll a 5 and

clip heads?

c. Find the probability: P(2 or 4 and tails)

2) Jack wants to redecorate his bedroom. He has

three paint color choices: white, green, and blue;

two bedspread choices: plaid and stripes; and

three posters: basketball, track, and soccer.

a. What is the size of the sample space for Jack

randomly choosing one paint color, one

bedspread, and one poster for his room?

b. Find the probability: P(green, plaid, and track)

c. What is the probability that Jack will randomly

choose a green or blue paint, a striped

bedspread, and a soccer team poster for his

room?

3) Omar has two kinds of pants: khaki and jeans,

and four different shirts: white, green, stripes, and

blue.

a. What is the sample space for Omar randomly

choosing an outfit?

b. What is the probability that Omar will

randomly choose jeans and a striped shirt?

c. Find the probability: P(khakis and solid color

shirt)

4) Jenna has a spinner with three sections lettered

A, B, and C; a number cube numbered 1-6; and a

bag containing the letters L, M, N, and Q.

a. How many possible outcomes are there for

spinning the spinner, rolling a number, and

drawing a letter out of the bag?

b. Find the probability: P(A, 3 and Q)

c. What is the probability that Jenna will spin a

B, roll not 6, and draw an L from the bag?

Mixed Review

5) Jerome has a 3

20 chance at winning the board

game he is playing. Write his chances of winning

the board game as a decimal.

6) Solve.

90 = 3z + 48

7) Minnie, Jocelyn, and Frank are running for class

president. Peter, Amy, Kayden, and Theo are

running for class vice president. What is the

probability that Frank and Kayden win the

election?

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Lesson 11.2.2 – Uniform Experimental Probability

Vocabulary

Theoretical probability Experimental probability

Active Instruction

ta(1) A carnival game has two spinners. Predict the

frequency of the outcomes if the game is played 200 times.

th(1) a) Find the theoretical probabilities for the

outcomes for rolling a number cube numbered 1-6. b) With your team, roll the number cube ten times. Individually record and graph the results. c) Report the results to your teacher. After your teacher has recorded all results, graph the results for the entire class. d) Compare and explain the similarities and differences between your team's results and the entire class's results.

ta(2) The same carnival game was played and the

results were recorded. Find the experimental probability.

Team Mastery

(3) You are rolling an octahedron numbered 1-8 and spinning a spinner with four sections labeled A, B, C, D. Predict

the number of times you will roll an even number and spin A in 500 trials.

Lesson Quick Look



Questions…


Today we found the experimental probability of events. Here’s an example! In a board game, each player flips a coin and spins the spinner.

First define the sample space.

S = {H1, H2, H3, T1, T2, T3}

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We see in the chart, that P(H and 3) has the same experimental and theoretical probability. Three

outcomes on the chart had higher experimental than theoretical probabilities and two outcomes had lower experimental than theoretical probabilities. You can expect that as the number of trials increases, the experimental probability will become closer to the theoretical probability. The experimental probability differs from the theoretical probability because of chance.


1) You have a number cube numbered from 1 to 6.

a. Find the theoretical probability for rolling a 6

as well as the probability for rolling a 1.

b. Predict how many of each outcome will

happen in 600 trials.

c. Below are the results of 600 trials. Compare

the predicted results to the actual results. Explain

your thinking.

2) You are rolling a decahedron numbered 1-10 and

spinning a spinner with three sections labeled X,

Y, and Z. Predict the number of times you will roll

a multiple of 5 and spin a Z in 700 trials.

3) You have a quarter and a dime each with heads

and tails.

a. Find the theoretical probabilities for each

outcome for flipping both coins.

4) Jenna has a spinner with three sections lettered

A, B, and C; a number cube numbered 1-6; and a

bag containing the letters L, M, N, and Q.

a. How many possible outcomes are there for

spinning the spinner, rolling a number, and

drawing a letter out of the bag?

b. Predict how many of each event will happen in

16 trials.

c. Toss the two coins and record the

frequencies. Remember each coin has a heads

and tails.

Outcome Frequency (16 Trials)

HH

HT

TH

TT

d. Find the experimental probabilities for your

experiment.

e. Compare the experimental probability to the

theoretical probability. Explain your thinking.

5) You have a dodecahedron numbered 1-12.

Predict the frequency of rolling an even number in

500 trials.

Mixed Review

6) Malia has 3 types of shoes: dress, boots, and

sneakers and 4 different socks: white, black, blue,

and striped in her suitcase. Write the theoretical

probability that she randomly chooses sneakers

and a solid color sock.

7) Find the probability of spinning the spinner as a

decimal.

P(not F)

Outcome Frequency (600 Trials)

6 98

1 99

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Lesson 11.2.3 – Non-Uniform Experimental Probability

Active Instruction

ta(1) A carnival game has some colored chips in a

bag. Find the probabilities for the outcomes of pulling chips out of the bag.

th(1) Select a cup that can be tossed into the air.

a) What are the possible outcomes for tossing the object? b) Predict the probability of each possible outcome. c) Toss the object and record the outcome for 40 trials. d) Write an experimental probability for each outcome. e) Predict the frequency for each outcome for 100 trials.

Team Mastery

(3) You will receive a bag with colored chips from

your teacher. b) Are the possibilities you wrote experimental or theoretical?

Lesson Quick Look



Questions…


Today we found the probability of events that did not have equally likely outcomes. Here’s an example! Miguel is playing a game. He has a bag that contains letters, but he cannot see what is in the bag. He performs an experiment to find the probabilities of pulling a letter out of the bag. He pulls out one letter and the replaces it 50 different times.

We can use this information to write the experimental probability for each event.

We can also use these probabilities to make predictions. Let’s say 1,000 people play this game. We can determine that roughly 0.24 • 1,000 = 240 people will select the letter Y.

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1) Ed recorded his results from flipping a quarter and

a nickel 500 times.

Outcome Frequency Experimental Probability

Quarter Heads and Nickel Heads

123

Quarter Heads and Nickel Tails

131

Quarter Tails and Nickel Heads

124

Quarter Tails and Nickel Tails

122

a) Write the experimental probability for each

outcome in the table.

b) If 100 people flip the coins, predict the number

of peope that will toss quarter heads-nickel tails.

2) A restaurant serves dinner each evening. One

evening, the manager recorded the sizes of the

dinner parties.

Party Size Frequency Probability

2 20

3 17

4 12

5 7

6 5

7 0

8 2

9 0

10 1

a) In the table, record the probability for

randomly waiting on a table for each party size.

b) Are the probabilities you wrote experimental

or theoretical? Explain your thinking.

c) If there are 300 dinner parties Monda-

Thursday, predict the number of parties that will

have eight people.

d) Which event is most likely?

Mixed Review

3) The Ezee Coffee C Shoppe offers the following to

its customers: three kinds of coffee (regular,

decaffeinated, and espresso); five kinds of

pastries (chocolate donuts, glazed donuts, apple

strudel, blueberry tart, and lemon squares) and

two kinds of sweetener (honey and sugar).

4) How many ways are there to order a coffee with a

sweetener and a pastry from the coffee shop?

5) Solve.

43g + 10 < 20

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Lesson 11.2.4 – Independent and Dependent Events

Vocabulary

Independent events Dependent events

Active Instruction

ta(1) You have a bag with 3 red and 2 blue marbles.

What is the probability of pulling a red marble? A blue marble?

th (1) The following number cards are placed in a bag: 1 one, 2 twos, 3 threes, 4 fours, and 5 fives. Each player pulls a number card out of the bag and keeps it. The first player to pull 2 fours wins.

a) Are the numbers pulled independent or dependent events? Explain your thinking. b) Senya and Zem are playing the game. Their results are recorded in the table below.

It is Zem's turn. What is the probability he will pull a four on the next turn?

Team Mastery (3) A bag of marbles has 20 marbles, 4 each of five

colors. Players take turns drawing a marble, writing down its color, and putting it back in the bag. The first player to draw 1 marble of each color is the winner. a) Are the marbles drawn independent or dependent events? Explain your thinking.

Lesson Quick Look



Questions…


Today we determine whether events are independent or dependent and found their probabilities.

For independent events, the probabilities do not change.

P(black marble) = 4

7

If I draw a marble and then put it back.

P(black marble) still equals 4

7.

For dependent events, the probabilities change.

P(white marble) = 3

7

If I draw a white marble and keep it

Then P(white marble) is now 2

6 or

1

3.

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1) Reneta is playing a game where she flips a coin.

When you flip the coin to heads 4 times in a row,

you win.

a) Is flipping the coin an independent or

dependent event? Explain your thinking.

b) Renata has flipped the coin three times, and it

has landed on heads each time. What is the

probability that it lands on heads a fourth time in a

row?

2) Antoine and Liza are drawing cubes from a bag.

The bag contains 3 yellow cubes, 2 red cubes,

and 5 green cubes. They keep the cubes they

draw after each turn. The first player to draw a

cube of each color wins.

a) Is drawing a cube an independent or

dependent event?

b) If Antoine draws a yellow cube on this first

turn, and Liza draws a green cube on her first

turn, what is the probability that Antoine will draw

another yellow cube on his second turn?

3) Hubert is rolling a number cube and spinning a

spinner. He wins when he rolls a 4 and spins

North.

a) Are rolling the cube and spinning the spinner

independent or dependent events?

b) If Hubert just rolled a 4 and spun South, what

is the probability that he will roll a 4 on his next

turn?

4) Greg has 4 salt bagels, 3 poppy seed bagels, and

4 plain bagels in a bag from which his coworkers

will randomly choose a bagel for a snack.

a) Is pulling out a bagel an independent or

dependent event? Explain your thinking.

b) One salt bagel and one poppy seed bagel

have already been randomly chosen. What is the

probability that the second bagel will be a poppy

seed bagel?

Mixed Review

5) Twenty-six out of 274 customers at a clothing

store this morning used a coupon. What is the

probability that the next customer uses a coupon

at the store?

6) A number cube has the following numbers on it: 4,

10, 15, 20, 22, 30. Describe P(<10) as impossible,

unlikely, equally likely, likely, or certain.

Unit 11 Cycle 1 Probability - · PDF fileUnit 11 Cycle 1 – Probability Lesson 11.1.3 ... Lesson 11.2.1 – Probability of Independent Compound Events

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