Name: ____________________________________________________

Module 6 - Statistics & Probability Notes & Classwork Packet Unit 11 Packet 1 - Calculating & Interpreting Probabilities

Standard Description

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers

indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor

likely, and a probability near 1 indicates a likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency,

and predict the approximate relative frequency given the probability.

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is

not good, explain possible sources of the discrepancy.

7.SP.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the

compound event occurs.

7.SP.8.B

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday

language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Lesson I can…

11.1 Describe the likelihood of an event.

11.2 Determine the experimental probability of a simple event.

11.3 Determine the theoretical probability of a simple event.

11.4 Compare and contrast experimental and theoretical probability of simple events.

11.5 Use a model to determine the theoretical probability of a compound event.

11.6 & 11.7 Determine the probability of a compound event.

SCHEDULE

Thursday

4/4

Friday

4/5

Monday

4/8

Tuesday

4/9

Thursday

4/11

Friday

4/12

Monday

4/15

11.1

HW: Page 1

11.2

HW: Page 2

11.3

HW: Page 3

11.4

HW: Page 4

11.5

HW: Page 5

11.6

HW: Page 6

11.7

HW: Page 7

This packet is due Tuesday 4/16

Module 5 & 6 Assessment is on Thursday 4/25

Packet Completion Rubric

4 3 2 1 0

Nothing in packet is missing.

Responses consistently meet

ALL of the criteria for high

quality work. Exemplary

effort is evident throughout

entire packet.

Packet is 75-100%

complete/accurate.

Work/effort misses the

criterion for high quality

consistently.

Packet is 50-75%

complete/accurate.

Work/effort has evidence

of quality but not

consistently.

More than 50% of the

packet is incomplete or

incorrect. Work does

not meet the expected

level of quality.

Packet is entirely

incomplete or not

turned in.

Grading Breakdown: 0 - 1.9 = F 2 - 2.4 = D 2.5 - 2.9 = C 3 - 3.4 = B 3.5 - 4 = A

Unit 11 Lesson 11.1

DO-NOW

1

Let’s Explore Probability!

When rolling a six-sided die, there are all sorts of possible outcomes of that event. In the graphic below, you

see several possible outcomes that may (or may not) be able to occur after rolling a die.

Do your best to find out the probability of each event occurring (You may express your answer as a fraction,

decimal, or percent.). Then, number the events from least likely (1) to most likely (9) in the boxes to the right.

2

Vocabulary

Term Definition Example

Experiment

Trial

Outcome

Event

Probability of an Event

Probability of an Event: measures the _________________________ that the event will occur.

Probability is a measure between __________________ as shown on the number line, and can be written

as a _____________________, a _____________________, or a ______________________.

To find the probability of an event, we start by setting up a fraction:

3

Finding the Probability of an Event (Example)

A pedestrian watching cars drive through an intersection notices that, of the 150 cars he watches go through

the intersection, 82 cars go straight, 17 cars go left, and 51 cars turn right. What is the probability that a car

at the intersection turns left?

P(car turns left) =

Try it Yo’ Self

Find each probability. Write your answer as a fraction, decimal, AND percent. Then, describe in words

the LIKELIHOOD of each event.

1. Picking a purple marble from a jar with 10 green marbles, 5 red marbles, 10 purple marbles, and 5

blue marbles.

2. Rolling a number greater than 4 on a standard die.

3. Landing on blue or purple on this spinner.

Complement of an Event

The complement of an event is the set of all outcomes in the sample space that are

________________________________in the event.

Finding the Complement of an Event (Example)

When rolling a number cube, the probability of rolling a 3 is written as P(rolling a 3). The

probability of rolling any number other than 3, or the complement of rolling a 3 is written as

P’(rolling a 3).

P(rolling a 3) =

P’(rolling a 3) or P(rolling a 1, 2, 4, 5, or 6) =

Finding the Complement of an Event (Example)

There are 2 red jacks in a standard deck of 52 cards. What is the probability of NOT getting a red jack if you

select one card at random? In other words, find the complement of pulling a red jack.

P’(red jack) =

4

Guided Practice

Problem Work Check ✓

1. What is the probability of spinning

of W?

2. What is the complement of

choosing a marble with diamonds?

3. A laundry basket has 24 socks in it.

Six are navy, 10 are black, and the

remaining are white. What is the

probability of drawing a white sock?

4. The spinner below

is spun. What is the

probability of

spinning an odd

number?

5. At the pediatrician’s office,

patients are able to draw a lollipop

from a jar after their checkup. The jar

contains 40 lollipops, 10 of which a

are blue, 15 of which are red, and 15

of which are yellow. What is the

probability of drawing a yellow

lollipop?

6. In the movie drawer, there are 7

action movies, 5 comedies, 3 dramas,

and 6 romances. What is the

probability of choosing a drama?

7. The letters in the word SOCCER

are put into a bag and drawn

randomly. What is the probability of

drawing a letter between A and M in

the alphabet?

8. A standard dice is rolled. What is

the complement of rolling a number

less than 3.

5

Unit 11 Lesson 11.2

DO-

NOW

For numbers 1-4: Find the probability of the event. Then, determine whether each event is

impossible, unlikely, as likely as not, likely, or certain.

1. You roll a six-sided number cube and the number is less than 2.

2. You roll two number cubes and the sum of the numbers is 1.

3. A bag contains 3 blue marbles and 3 red marbles. You select a red marble from the bag at

random.

4. A spinner has 5 equal sections marked 1 through 5. You spin and land on a number less

than 5.

5. There are 4 aces in a standard deck of 52 cards. What is the probability of not getting an

ace? In other words, what is the complement?

Bottle Flipping (...Sooooo Last Year)

Today in class, you’re going to try your hand at the newest rage: flipping a cup to see if you can get it to land

on the top, side, or bottom.

Your Task: Start with the cup standing upright at the edge of the table so that part of the base is slightly off

the edge. Then, flip the cup while lifting the bottom edge and see if the cup lands:

1. Open end up

2. Open end down

3. On its side

Step 1: Complete 20 trials of this experiment and record your data in the table below using tally marks.

Open end up Open end down On its side

Step 2: After collecting your data, complete the reflection questions on the following page.

6

Calculating Experimental Probability

You can use ___________________________________ to approximate the probability of an event.

Experimental Probability: The ______________________________ the event occurs compared to

the _____________________________. We express experimental probability as a fraction.

Simple Event: A _________________ experiment that results in only ____________ outcome

(For example: The probability of rolling a 4 on a number cube).

7

Try it Out!

Martin has a bag of marbles. He removed one marble at random, recorded the color and then placed it back

in the bag. He repeated this process several times and recorded his results in the table. Find the

experimental probability of drawing each color.

Step 1: Identify the total number of trials _______________________________

Step 2: Complete the table of experimental probabilities. Write each answer as a fraction in simplest

form.

Color Experimental Probability

Red

Blue

Green

Yellow

Guided Practice - Spin the Wheel!

Part 1: Make a Prediction

In this experiment, you’ll spin a wheel with 12 equally sized wedges. Each wedge is labeled with a number

between 1 and 12. Using your newfound knowledge of probability, calculate the likelihood of the wheel

landing on…

The wedge labeled 1: _______

The wedge labeled 10: _______

A wedge labeled with an even number: _______

8

Part 2: Collect Data

You will now perform an experiment to compare the probabilities you found in part 1 with actual

experimental results. Your teacher will spin the wheel 40 times. Your job is to record the outcome of each

spin in the data table below (use tally marks).

1 2 3 4 5 6

7 8 9 10 11 12

Part 3: Calculate Experimental Probability

Using your data from the table above, calculate the EXPERIMENTAL probability of the spinner landing on

each number.

1 2 3 4 5 6

7 8 9 10 11 12

Part 4: Reflect

Compare your experimental probabilities to the theoretical probabilities you calculated in part 1. Were they

the same? How could you explain the differences you observed?

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

9

Unit 11 Lesson 11.3

DO-NOW 1. A bag contains cutouts with the number of shapes listed in the table to the right. Find

the following probabilities.

P(Circle) =

P’(Triangle) =

P(Not a Circle) =

2. Michelle and Joan are on the same softball team. This year, Michelle got 8 hits out of 48

times at bat, while Joan got 12 hits out of 40 times at bat. Who do you think is more

likely to get a hit in her next time at bat? Explain using your understanding of

probability.

Exploring Theoretical Probability

At a school fair, you have a choice of spinning Spinner A or Spinner B. You win an MP3 player if the spinner

lands on a section with a star in it. Which spinner should you choose if you want a better chance of winning?

a. Complete the table below.

10

b. Compare the ratios for Spinner A and Spinner B by completing the sentences below.

i. The ratio for Spinner __________ is greater than the ratio for Spinner __________.

ii. I should choose _______________________ for a better chance of winning.

c. Reflect: Theoretical probability is a way to describe how you found the chance of winning an MP3

player in the scenario above. Using the spinner example to help you, explain in your own words how

to find the theoretical probability of an event.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

Finding Theoretical Probability

Theoretical Probability: A comparison of the number of times the event _________________ occur to

the total number of _______________________________.

Finding Theoretical Probability (Example)

A bag contains 6 red marbles and 12 blue ones. You select one marble at random from the bag. What is the

theoretical probability that you select a red marble? Write your answer in simplest form.

Step 1: Find the number of ways the event can occur, that is, the number of red marbles: _______

Step 2: Add to find the TOTAL number of possible outcomes. __________________________

Step 3: Find the probability of selecting a red marble.

Comparing Theoretical & Experimental Probabilities

Experimental Probability calculates…

what ACTUALLY happened

(Last Lesson)

Theoretical Probability calculates…

what is EXPECTED to happen

(This Lesson)

11

Guided Practice - Comparing Theoretical and Experimental Probability

Six students are performing in a talent contest. Each student rolls a number cube to determine the order of

the performances. One of the students is wondering what her chances are of rolling the highest number (6).

Let’s help her find out!

Step 1: Complete the table of theoretical probabilities for the 6 possible outcomes.

Now we’ll perform an experiment to determine her experimental probability of rolling a 6.

Step 2: Roll a number cube 30 times. Complete the table for the frequency of each number and then

find it’s experimental probability. (Frequency just means number of times you land on each number)

How do theoretical and experimental probabilities compare?

Step 3: Look at the tables you completed. How do your experimental probabilities compare to your

theoretical?

_____________________________________________________________________

_____________________________________________________________________

By performing more trials in an experiment, you tend to get experimental probabilities that are closer to the

theoretical probabilities.

Step 4: Combine your table from step 2 with two of your classmates’ tables. Now you will calculate

experimental probability using 90 total trials. Are your new experimental probabilities closer to the

theoretical probabilities your calculated in step 1?

12