geometry unit 11 note sheets date name of...

Geometry Unit 11 Note Sheets

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Date Name of Lesson

OC 11.1, 13.1 Set Theory and Sample Space

AB 11.1 Experimental Probability Dice Activity pt 1

Theoretical Probability Dice Activity pt 2

Probability Activity # 1 – Pig

13.3 Geometric Probability

Quiz

OC 11.7, 11.8, 13.5 Independent and Dependent Events

OC 11.5, 13.6 Mutually Exclusive Events

OC 11.6 Conditional Probability and Two-Way Tables

Quiz

Review of Probability

Practice Test

Unit 11 Test


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OC 11.1, 13.1 Set Theory and Sample Space Notes Sheet You will see that set theory is useful in calculating probabilities. A set is a well-defined collection of distinct

objects. Each object in a set is called an element of the set. A set may be specified by writing its elements in

braces. For example, the set S of prime numbers less than 10 may be written as S = {2, 3, 5, 7}.

The number of elements in a set S may be written as n(S). For the set S of prime numbers less than 10, n(S) = 4.

The set with no elements is the empty set and is denoted by Ø or { }. The set of all elements under

consideration is the universal set and is denoted by U. The following terms describe how sets are related to

each other.

Discuss: For any set A, what is A ∩ Ø? Explain.

__________________________________________________________________________________________

__________________________________________________________________________________________

Vocabulary:

Sample Space ______________________________________________________________________________

Tree Diagram ______________________________________________________________________________

Guided Practice

Represent the sample space for this experiment by making an organized list, a table, and a tree diagram.

1. A coin is tossed twice.

Your Turn

2. Brooke could take a summer job in California or Arizona at a hotel or a bed-and-breakfast.


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Guided Practice

3. To take a hamburger order, Anthony asks each customer the questions from the script:

What size burger would you like: kid’s, regular, or large?

Would you like cheese on that?

Would you like tomato and/or pickles?

Draw a tree diagram to represent the sample space for hamburger orders.

Fundamental Counting Principle

Guided Practice

4. Esmeralda has selected a size and overall style for her class ring. Now she must choose from the rind

options shown. How many different rings could Esmeralda create in her chosen style and size?

Your Turn

5. New cars are available with a wide selection of options for the consumer. One options is shown from

each category shown. How many different cars could a consumer create in the chosen make and model?


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Experimental Probability vs. Theoretical Probability Tally the rolls below. Pay attention to the color of the dice. White dice

Divide the totals above by the total number of trials to get the experimental

probabilities.

C

o

l

o

r

e

d

D

i

c

e

C

o

l

o

r

e

d

D

i

c

e

Total number of

trials__________________


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Please tally the sum of the dice in the chart below and then compute the

experimental probability for each sum.

Frequency: Sum of Two Dice Exp. Prob.

2

3

4

5

6

7

8

9

10

11

12


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AB 13.1 Theoretical and Experimental Probability Notes Sheet Vocabulary:

Probability of an Event ______________________________________________________________________

__________________________________________________________________________________________

Theoretical Probability

Define:

Calculate:

Guided Practice

1. Adam and Alan design T-shirts with silk screened emblems, and are selling the T-shirts to raise money.

The table below shows the number of T-shirts they have and each design. A customer chooses a T-shirt

at random. What is the probability that the customer chooses a red T-shirt?

Gold emblem Silver emblem

Green T-shirt 10 8

Red T-shirt 6 6

2. From the above example, what is the probability that the customer chooses a T-shirt with a gold

emblem?

Your Turn

3. The spinner is divided into sections with the same area. What is the probability that the spinner stops on

a multiple of 3?


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Experimental Probability

Define:

Calculate:

Guided Practice

4. Each section of the spinner shown has the same area. The spinner was spun 20 times. The table shows

the results. For which color is the experimental probability of stopping on the color the same as the

theoretical probability?

Spinner Results

Red Green Blue Yellow

5 9 3 3

Your Turn

5. A bag contains one blue, one green, one yellow, and one red ball. A ball is drawn at random from the

bag and then replaced. The table shows the results for 24 drawings. For which color ball is the

experimental probability of drawing the color the same as the theoretical probability?

Guided Practice

A survey asked a total of 600 students (100 male students and 100 female students who were 11, 13, and 15

years old) about their exercise habits. The table shows the number of students who said they exercise 2 hours or

more each week.

6. What is the probability that a randomly selected female student who participated in this study exercises

2 hours or more each week?

Your Turn

7. What is the probability that a randomly selected 15-year-old student who participated in this survey

exercises 2 hours or more each week?

8. What is the probability that a randomly selected student who participated in the survey exercise 2 or

more hours each week?

11 years 13 years 15 years

Female 53 57 51

Male 65 68 67


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13.3 Geometric Probability Notes Sheet Vocabulary

Geometric Probability _______________________________________________________________________

Length Probability Ratio

Guided Practice

Point X is chosen at random on 𝐽𝑀̅̅ ̅̅ .

1. Find the probability that X is on 𝐾𝐿̅̅ ̅̅ .

2. 𝑃(𝑋 𝑖𝑠 𝑜𝑛 𝐾𝑀̅̅ ̅̅ ̅)

Your Turn

3. Point Z is chosen at random on 𝐴𝐷̅̅ ̅̅ . Find the probability that Z is on 𝐴𝐶̅̅ ̅̅ .

Guided Practice

4. A Chicago Transit Authority train arrives or departs a station like Addison on the Red Line every 15

minutes. Assuming you arrive at Addison on the Red Line at a random time, what is the probability that

you will have to wait 5 or more minutes for a train?

Your Turn

5. Iced tea at a cafeteria-style restaurant is made in 8-gallon containers. Once the level gets below 2

gallons, the flavor of the tea becomes weak. What is the probability that when someone tries to pour a

glass of tea from the container, it will have a weak flavor?


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Area Probability Ratio

Guided Practice

6. Joey is shooting a paintball gun at the target. What is the probability that he will short the shaded

region?

Your Turn

7. If Mariah threw 10 beanbags at the board, what is the probability that the beanbag went in the hole?

Guided Practice

Use the spinner to find each probability.

8. P(pointer landing on section 3)


Your Turn




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OC 11.7, 11.8, 13.5 Independent and Dependent Events Notes Sheet Vocabulary

Compound Event ___________________________________________________________________________

Independent Events _________________________________________________________________________

Dependent Event ___________________________________________________________________________

Guided Practice

Determine whether the events are independent or dependent. Explain your reasoning.

1. One coin is tossed, and then a second coin is tossed.

2. Wednesday’s lottery numbers and Saturday’s lottery numbers.

3. Jared selects a shirt from his closet to wear on Monday and then a different shirt to wear on Tuesday.

Your Turn

4. A card is selected from a deck of cards and not put back. Then a second card is selected.

5. A die is rolled, and then a second die is rolled.

Probability of Two Independent Events

Define

Symbols

Guided Practice

6. Eric and his friends are going to a concert. They put three blue and five yellow slips of paper into a bag.

If a person draws a yellow slip, he or she will ride in the van to the concert. A blue slip means he or she

rides in the car.

Suppose Eric draws a slip. Not liking the outcome, he puts it back and draws a second time. What is

the probability that on each draw his slip is blue?


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Your Turn

7. Brad and Rick are going out to lunch. They put 5 green slips of paper and 6 red slips of paper into a

bag. If a person draws a green slip, they will order a hamburger. IF they draw a red slip, they will order

a pizza.

Suppose that Brad draws a slip. Not liking the outcome, he puts it back and draws a second time. What

is the probability that on each draw his slip is green?

Probability of Two Dependent Events

Define

Symbols

Conditional Probability ______________________________________________________________________

Probability Tree ____________________________________________________________________________

Guided Practice

8. Using the example with Eric and the concert. Supposed Eric draws a slip and does not put it back. Then

his friend Alec draws a slip. What is the probability that both friends draw a yellow slip?

Your Turn

9. Using the example with Brad and Rick eating lunch. Suppose Brad draws a slip and does not put it

back. Then Rick draws a slip. What is the probability that both will draw a green slip?


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OC 11.5, 13.6 Mutually Exclusive Events Notes Sheet Vocabulary

Mutually Exclusive _________________________________________________________________________

Guided Practice

Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning.

1. a junior winning the election or a senior winning the election

2. a sophomore winning the election or a female winning the election

3. drawing an ace or a club from a standard deck of cards

Your Turn

4. drawing a card from a standard deck of cards and getting a 5 or a heart

5. getting a sum of 6 or 6 when two dice are rolled

Probability of Mutually Exclusive Events

Define

Symbols

Guided Practice

6. Molly makes a playlist that consists of songs from three different albums by her favorite artist. If she

lets her MP3 player select the songs from this list at random, what is the probability that the first song is

from Album 1 or Album 2?

Your Turn

7. Leo reaches into a can that contains 30 quarters, 25 dimes, 40 nickels and 15 pennies. What is the

probability that the first coin he picks is a quarter or a penny?

Molly’s Playlist

Album Number of Songs

1 10

2 12

3 13


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Probability of Events That Are Not Mutually Exclusive Events

Define

Symbols

Guided Practice

8. The table shows the number and type of

paintings that Timothy has created. If he

randomly selects a painting to submit to an art

contest, what is the probability that he selects a

portrait or an oil painting?

Your Turn

9. What is the probability that Timothy selects a watercolor or a landscape?

Complement _______________________________________________________________________________

Probability of the Complement of an Event

Define

Symbols

Guided Practice

10. Brittany bought 20 raffle tickets, hoping to win the $1,000 gift card to her favorite clothing store. If a

total of 300 raffle tickets were sold, what is the probability that Brittany will not win the gift card?

Your Turn

11. Miguel bought 15 chances to pick the one red marble from a container to win a gift certificate to the

bookstore. If there is a total of 200 marbles in the container, what is the probability that Miguel will not

win the gift certificate?

Timothy’s Paintings

Media Still Life Portrait Landscape

watercolor 4 5 3

oil 1 3 2

acrylic 3 2 1

pastel 1 0 5


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OB 11.6 Conditional Probability and Two-Way Tables Notes Sheet Vocabulary

Conditional Probability ______________________________________________________________________

1 EXAMPLE Finding Conditional Probabilities

One hundred people who frequently get migraine headaches

were chosen to participate in a study of a new anti-headache

medicine. Some of the participants were given the

medicine; others were not. After one week, the participants

were asked if they got a headache during the week. The

two-way table summarizes the results.

A To the nearest percent, what is the probability that a participant who took the medicine did not get

a headache?

Let event A be the event that a participant took the medicine. Let event B be the event that a participant did

not get a headache.

To find the probability that a participant who took the medicine did not get a headache, you must find P(B |

A). You are only concerned with participants who took the medicine, so look at the data in the “Took

Medicine” column.

There were participants who took the medicine.

Of these participants, participants did not get a headache.

So, P(B | A) = = .

B To the nearest percent, what is the probability that a participant who did not get a headache took

the medicine?

To find the probability that a participant who did not get a headache took the medicine, you must find P(A |

B). You are only concerned with participants who did not get a headache, so look at the data in the “No

headache” row.

There were participants who did not get a headache.

Of these participants, participants took the medicine.

So, P(A | B) ≈ .

REFLECT

1a. In general, do you think P(B | A) = P(A | B)? Why or why not?

Took

Medicine

No

Medicine TOTAL

Headache 12 15 27

No

Headache 48 25 73

TOTAL 60 40 100


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Conditional Probability

define

formula

3 EXAMPLE Using the Conditional Probability Formula

In a standard deck of playing cards, find the probability that a red card is a queen.

A Let event Q be the event that a card is a queen. Let event R be the event that a card is red. You are asked to

find P(Q | R). First find P(R ∩ Q) and P(R).

R ∩ Q represents cards that are both red and a queen; that is, red queens.

There are red queens in the deck of 52 cards, so P(R ∩ Q) = .

There are red cards in the deck, so P(R) = .

B Use the formula for conditional probability.

P(Q | R) =

Substitute probabilities from above.

= Multiply numerator and denominator by

52.

= Simplify.

So, the probability that a red card is a queen is . REFLECT

3a. How can you interpret the probability you calculated above?

3b. Is the probability that a red card is a queen equal to the probability that a queen is red? Explain.

In Exercises 4–6 consider a standard deck of playing cards and the following events: A: the card is an

ace; B: the card is black; C: the card is a club. Find each probability as a fraction.

4. P(C | A)

5. P(B | C)

6. P(C | B)

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