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Geometry

Probability

2015-10-28

www.njctl.org

http://www.njctl.org

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Table of Contents

Probability of Simple Events

Probability and Length

Probability and Area

Click on a topic to go to that section

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Throughout this unit, the Standards for Mathematical Practice are used.

MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.

Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.

If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

(Answer) / 66

Throughout this unit, the Standards for Mathematical Practice are used.

MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.

Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.

If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

[This object is a pull tab]

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Probability of Simple Events

Return to Table of Contents

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A sample space is a set of ALL possible outcomes for an activity or experiment.

A sample space is usually denoted using set notation {...} and the possible outcomes are listed as elements in the set

{a, b, c, ... z}.

Sample Space

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Find the sample space in the box below each activity.

{yellow, blue, red, green}

H = headsT = tails

{HH, HT, TH, TT}

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

{yellow, green, red}

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

Sample Space

Click to Reveal Click to

Reveal

Click to

RevealClick to

RevealClick to

Reveal

(Answer) / 66

Find the sample space in the box below each activity.

{yellow, blue, red, green}

H = headsT = tails

{HH, HT, TH, TT}

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

{yellow, green, red}

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

Sample Space

Click to Reveal Click to

Reveal

Click to

RevealClick to

RevealClick to

Reveal


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Questioning to help address MP standards:What information do you have? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) What does the term "sample space" mean? (MP6)Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)

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If the outcomes in a sample space are equally likely to occur, the theoretical probability of an event P(event) is a numerical

value from 0 to 1 that measures the likelihood of an event. You can write the probability of an event as a ratio, decimal or a percent.

P(event) = number of favorable outcomes number of possible outcomes

· An event with a probability close to 0 is unlikely to occur.· An event with a probability close to 1 is likely to occur.

· An event with a probability of 0.5 is just as likely to occur as not.

Impossible CertainEqually Likely to Occur

or not Occur

0 less likely 0.5 more likely 1

Theoretical Probability

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There are 7 red marbles and 3 green marbles in a bag. One marble is chosen at random.

Write the probability that a green marble is chosen.

P(Green)

Write as a fraction Write as a decimal Write as a percent

Non - Geometric Examples

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There are 7 red marbles and 3 green marbles in a bag. One marble is chosen at random.

Write the probability that a green marble is chosen.

P(Green)

Write as a fraction Write as a decimal Write as a percent

Non - Geometric Examples


Ans

wer

3/10 = 0.3 = 30%

Questioning to help address MP standards:What information do you have? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)

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P(card) = 1/ 52

Suppose you choose a card from the deck. What is ....

P(Heart) = ______ P(3) = ______ P(4 of Spades) = ______

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P(card) = 1/ 52

Suppose you choose a card from the deck. What is ....

P(Heart) = ______ P(3) = ______ P(4 of Spades) = ______[This object is a pull tab]

Ans

wer

P(Heart) = 1/4P(3) = 1/13P(4 of spades) = 1/52

Questioning to help address MP standards:What information do you have? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does anyone have the same answer, but a different way to explain it? (MP7)Can you find a shortcut to solve the problem? How would your shortcut make the problem easier? (MP8)- Ans using 1st solution: There are only 4 suits & 1 of them is a heart, so P(Heart) = 1/4

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P(2) = _______

P(even) = _______

P(prime) = _______

P(> 4) = _______

Probability

2. Find the probability of each event.

1. Find the sample space for the activity below.

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P(2) = _______

P(even) = _______

P(prime) = _______

P(> 4) = _______

Probability




Ans

wer

Questioning to help address MP standards:What does "sample space" mean? (MP6)What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)

{1, 2, 3, 4, 5, 6}P(2) = 1/6P(even) = 1/2P(prime) = 1/2P(> 4) = 1/3

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P(green) = _______

P(orange) = _______


Probability

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P(green) = _______

P(orange) = _______


Probability


Ans

wer


{purple, green, orange, red}

P(green) = 1/4

P(orange) = 1/4

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P(heads) = _______

P(tails) = _______



Probability

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P(heads) = _______

P(tails) = _______



Probability


Ans

wer

{H, T}

P(heads) = 1/2

P(tails) = 1/2


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1 A multiple choice question has 14 possible answers, only one of which is correct. Is it "unlikely" to answer a question correctly if a random guess is made? Yes

No

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1 A multiple choice question has 14 possible answers, only one of which is correct. Is it "unlikely" to answer a question correctly if a random guess is made? Yes

No


Ans

wer

YES

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2 What is the sample space for flipping a coin twice?

A HT, TH

B HH, HT, TH, TT

C HH, HT, TT

D HH, TT, HT, HT

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2 What is the sample space for flipping a coin twice?

A HT, TH

B HH, HT, TH, TT

C HH, HT, TT

D HH, TT, HT, HT


Ans

wer

B

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3 What is the sample space for flipping a coin 3 times?

A HHH, TTT, THT, HTH, HHT, TTH, HTH

B HHH, HTT, HTH, TTT, HTT, THH, HHT, THTC HTT, THT, HTH, HHH, TTH, TTT

D HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

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3 What is the sample space for flipping a coin 3 times?

A HHH, TTT, THT, HTH, HHT, TTH, HTH

B HHH, HTT, HTH, TTT, HTT, THH, HHT, THTC HTT, THT, HTH, HHH, TTH, TTT

D HHH, HHT, HTH, HTT, THH, THT, TTH, TTT


Ans

wer

D

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4 On a multiple choice test, each question has 4 possible answers. If you make a random guess on the first question, what is the probability that you are correct? A 4

B 1

C 1/4

D 0

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4 On a multiple choice test, each question has 4 possible answers. If you make a random guess on the first question, what is the probability that you are correct? A 4

B 1

C 1/4

D 0


Ans

wer

C

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5 A die with 12 sides is rolled. What is the probability of rolling a number less than 11? A 1/12

B 10

C 5/6

D 11/12

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5 A die with 12 sides is rolled. What is the probability of rolling a number less than 11? A 1/12

B 10

C 5/6

D 11/12


Ans

wer

C

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6 What is the probability of rolling a number greater than 2 on a number cube?

A 1/6

B 1/3

C 1/2

D 2/3

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6 What is the probability of rolling a number greater than 2 on a number cube?

A 1/6

B 1/3

C 1/2

D 2/3


Ans

wer

D

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7 What is the probability of randomly choosing a science book from a shelf that holds 3 mystery books, 5 science books and 4 nature books?

A 1/4

B 1/3

C 5/12

D 7/12

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7 What is the probability of randomly choosing a science book from a shelf that holds 3 mystery books, 5 science books and 4 nature books?

A 1/4

B 1/3

C 5/12

D 7/12


Ans

wer

C

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8 A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A 1/3

B 3/16 C 1/13 D 1/7

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8 A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A 1/3

B 3/16 C 1/13 D 1/7


Ans

wer

B

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We have evaluated probabilities by counting thenumber of favorable outcomes and dividing that number by the total number of possible outcomes.

In the rest of this unit, you will use a related process in which the division involves geometric measures such as length or area. This process is called geometric probability.

click to reveal

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Probability and Length


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Using Segments to Find Probability

A B C D

Point K on AD is chosen at random. The probability that K is on BC is the ratio of the length of BC to the length of AD.

P(K on BC) = BC AD

Fill in the blanks.

P(K on AC) = P(K on AB) = AD

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A B C D

Point K on AD is chosen at random. The probability that K is on BC is the ratio of the length of BC to the length of AD.

P(K on BC) = BC AD

Fill in the blanks.

P(K on AC) = P(K on AB) = AD


Ans

wer

AC

AB AD

Questioning to help address MP standards:How is P(K on AC) related to P(K on BC)? (MP7)How is P(K on AB) related to P(K on BC)? (MP7)

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2 3 4 5 6 7 8 9 10 11 12 13 14

S Q R T

Point H on ST is selected at random. What is the probability that H lies on SR?

Step 1: Find the length of each segment.

length of SR = ____________ length of ST = ____________


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2 3 4 5 6 7 8 9 10 11 12 13 14

S Q R T


Step 1: Find the length of each segment.

length of SR = ____________ length of ST = ____________



Ans

wer SR = 6

ST = 12

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2 3 4 5 6 7 8 9 10 11 12 13 14

S Q R T


Step 2: Find the probability.

P(H on SR) = _______________

The probability is _______ or _________% .


(Answer) / 66

2 3 4 5 6 7 8 9 10 11 12 13 14

S Q R T



P(H on SR) = _______________




Ans

wer P(H on SR) = 1/2

0.5 or 50%

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A B C D E F G H I J K L M

0 1 2 3 4 5 6 7 8 9 10 11 12

JL = __________

A point on AM is chosen at random. Find the probability that the point lies on the given segment.

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0 1 2 3 4 5 6 7 8 9 10 11 12

JL = __________



Ans

wer

1/6 or 0.17 or 17%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of JL related to the probability that a point lies on JL? (MP7)

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0 1 2 3 4 5 6 7 8 9 10 11 12


DJ = __________


(Answer) / 66


0 1 2 3 4 5 6 7 8 9 10 11 12


DJ = __________



Ans

wer

1/2 or 0.5 or 50%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of DJ related to the probability that a point lies on DJ? (MP7)

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0 1 2 3 4 5 6 7 8 9 10 11 12


BE = __________


(Answer) / 66


0 1 2 3 4 5 6 7 8 9 10 11 12


BE = __________



Ans

wer

1/4 or 0.25 or 25%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of BE related to the probability that a point lies on BE? (MP7)

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0 1 2 3 4 5 6 7 8 9 10 11 12


AJ = __________


(Answer) / 66


0 1 2 3 4 5 6 7 8 9 10 11 12


AJ = __________



Ans

wer

3/4 or 0.75 or 75%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of AJ related to the probability that a point lies on AJ? (MP7)

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0 1 2 3 4 5 6 7 8 9 10 11 12

Using Segments to Find ProbabilityA point on AM is chosen at random. Find the probability that the point lies on the given segment.

CK = __________

(Answer) / 66


0 1 2 3 4 5 6 7 8 9 10 11 12


CK = __________[This object is a pull tab]

Ans

wer

2/3 or 0.67 or 67%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of CK related to the probability that a point lies on CK? (MP7)

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0 1 2 3 4 5 6 7 8 9 10 11 12


BL = __________

(Answer) / 66


0 1 2 3 4 5 6 7 8 9 10 11 12


BL = __________


Ans

wer

5/6 or 0.83 or 83%

Questioning to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)How is the length of BL related to the probability that a point lies on BL? (MP7)

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In the figure at the right = .

What is the probability that a point chosen at random on AC will lie on BC? Explain.

ABBC

1 2

A B C


If AB = x, then BC = 2x and AC = 3x.

BC/AC = 2x/3x = 2/3

Since have a ratio given to us, can we use algebraic expressions to represent this information?

Now, can we determine the ratio to represent the probability that a point chosen at random on AC will lie on BC?

click

click

(Answer) / 66

In the figure at the right = .

What is the probability that a point chosen at random on AC will lie on BC? Explain.

ABBC

1 2

A B C


If AB = x, then BC = 2x and AC = 3x.

BC/AC = 2x/3x = 2/3

Since have a ratio given to us, can we use algebraic expressions to represent this information?

Now, can we determine the ratio to represent the probability that a point chosen at random on AC will lie on BC?

click

click


Mat

h Pr

actic

eQuestions on this slide address MP standards:

Question #1: MP2 & MP4Question #2: MP2

Additional Q's to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) How is the length of BC related to the probability that a point lies on BC? (MP7)Explain what you did to solve the problem. (MP6)

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A point between A and B on each number line is chosen at random. What is the probability that the point is between C and D?

A)

D)C)

B)

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B


(Answer) / 66

A point between A and B on each number line is chosen at random. What is the probability that the point is between C and D?

A)

D)C)

B)

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B

0 1 2 3 4 5 6 7 8

A C D B



Ans

wer

A) 5/8

B) 3/8

C) 1/2

D) 1/4

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Real-World Example

A commuter train runs every 25 minutes. If a commuter arrives at the station at a random time, what is the probability that the commuter will have to wait no more than 5 minutes for the train?

(Answer) / 66

Real-World Example

A commuter train runs every 25 minutes. If a commuter arrives at the station at a random time, what is the probability that the commuter will have to wait no more than 5 minutes for the train?


Mat

h Pr

actic

eQuestion on this slide address MP standards:

MP2 & MP4

Additional Q's to help address MP standards:What information are you given? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) Would it help to draw a picture? What would you draw? (MP 4 & MP5)What do you know about line segments and probability based on length that you can apply to this situation? (MP7)

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Real-World ExampleWhich diagram models the situation? (Each number on the number line represents the number of minutes remaining before the next train leaves.)

0 5 10 15 20 25

D C E

0 5 10 15 20 25

D C E

0 5 10 15 20 25

D C EA) B) C)

Find the probability.

P(waiting no more = _______ than 5 minutes)

(Answer) / 66

Real-World ExampleWhich diagram models the situation? (Each number on the number line represents the number of minutes remaining before the next train leaves.)

0 5 10 15 20 25

D C E

0 5 10 15 20 25

D C E

0 5 10 15 20 25

D C EA) B) C)

Find the probability.

P(waiting no more = _______ than 5 minutes)


Ans

wer

B

1/5 or 20%

Questions on this slide address MP standards:Question 1 (about diagram): MP4 & MP5

Additional Q's to help address MP standards:What is this problem asking? (MP1)What strategies are you going to use? (MP1) Can you do this mentally? (MP1)Does your answer seem reasonable? Why or why not? (MP3)

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A fitness club set up an express exercise circuit. To warm up, a person works out on weight machines for 90 s. Next, the person jogs in place for 60 s, and then takes 30 s to do aerobics. After this, the cycle repeats. If you enter the express exercise circuit at a random time, what is the probability that a friend of yours is jogging in place? What is the probability that your friend will be on the weight machines?

Real-World Example

(Answer) / 66

A fitness club set up an express exercise circuit. To warm up, a person works out on weight machines for 90 s. Next, the person jogs in place for 60 s, and then takes 30 s to do aerobics. After this, the cycle repeats. If you enter the express exercise circuit at a random time, what is the probability that a friend of yours is jogging in place? What is the probability that your friend will be on the weight machines?

Real-World Example


Ans

wer

P(jogging in place) = 1/3 or 33%

P(weight machines) = 1/2 or 50%

Question on this slide address MP standards:MP2 & MP4


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At the space museum theater, a movie runs for 15 min. There are 5 min between shows. If you enter the theater at a random time, what is the probability that you will have to wait more than 2 min for the next movie to start?

Real-World Example

(Answer) / 66

At the space museum theater, a movie runs for 15 min. There are 5 min between shows. If you enter the theater at a random time, what is the probability that you will have to wait more than 2 min for the next movie to start?

Real-World Example


Ans

wer

18/20 or 90%



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Real-World Example

A Sunday night sports show is on from 10:00 p.m. to 10:30 p.m. You want to find out if your favorite team won last weekend but forgot that the show had already started. You turn it on at 10:14 p.m. The score is announced at one random time during the show. What is the probability that you haven't missed the repost about your favorite team?

(Answer) / 66

Real-World Example

A Sunday night sports show is on from 10:00 p.m. to 10:30 p.m. You want to find out if your favorite team won last weekend but forgot that the show had already started. You turn it on at 10:14 p.m. The score is announced at one random time during the show. What is the probability that you haven't missed the repost about your favorite team?


Ans

wer

8/15 or 53%



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9 Point X on QT is chosen at random. What is the probability that X is on ST?A QT

ST B ST

QT

C QSST

D STQS

Q R

S T

(Answer) / 66

9 Point X on QT is chosen at random. What is the probability that X is on ST?A QT

ST B ST

QT

C QSST

D STQS

Q R

S T


Ans

wer

B

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10 What is the probability that a point chosen at random from EH will be on EF?

A 1/3

B 3

C 1/4

D 3/4

3 cm 5 cm 4cm

E F G H

(Answer) / 66

10 What is the probability that a point chosen at random from EH will be on EF?

A 1/3

B 3

C 1/4

D 3/4

3 cm 5 cm 4cm

E F G H


Ans

wer

C

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11 If AC = 10, what is the probability that a point chosen at random from AC will land on BC?

A 3/5

B 2/5

C 2/3

D 1/2

A B C

6 in

(Answer) / 66

11 If AC = 10, what is the probability that a point chosen at random from AC will land on BC?

A 3/5

B 2/5

C 2/3

D 1/2

A B C

6 in


Ans

wer

B

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12 Find the probability that a point chosen at random on AE is on BD.

A 20%

B 25%

C 30%

D 35%

E 40%

A B C D E F

0 4 8 12 16 20 24

(Answer) / 66

12 Find the probability that a point chosen at random on AE is on BD.

A 20%

B 25%

C 30%

D 35%

E 40%

A B C D E F

0 4 8 12 16 20 24


Ans

wer

D

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13 Point P on AD is chosen at random. For which of the figures below is the probability that P is on BC 25%? Note: Diagrams not drawn to scale.

A

B

C

DA B C D

2 5 8 10

A B C D

2 3 4 5

A B C D

1 2 3 4

A B C D

1 2 3 5

(Answer) / 66

13 Point P on AD is chosen at random. For which of the figures below is the probability that P is on BC 25%? Note: Diagrams not drawn to scale.

A

B

C

DA B C D

2 5 8 10

A B C D

2 3 4 5

A B C D

1 2 3 4

A B C D

1 2 3 5


Ans

wer

A

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14 You have a 7-cm straw and a 10-cm straw. You want to cut the 10-cm straw into two pieces so that the three pieces make a triangle. If you cut the straw at a random point, what is the probability that you can make a triangle?

A 30%

B 40%

C 60%

D 70%

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14 You have a 7-cm straw and a 10-cm straw. You want to cut the 10-cm straw into two pieces so that the three pieces make a triangle. If you cut the straw at a random point, what is the probability that you can make a triangle?

A 30%

B 40%

C 60%

D 70%


Ans

wer

D

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Probability and Area


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AC

Using Area to Find ProbabilityPoint B in region A is chosen at random. The probability that point B is in region C is the ratio of the area of region C to the ratio of the area of region A.

P(B in region C) = area of region C area of region A

Find the probability for the given areas.

area of region A = 24 in2 area of region C = 3 in2

P(B in region C) = ________

(Answer) / 66

AC

Using Area to Find ProbabilityPoint B in region A is chosen at random. The probability that point B is in region C is the ratio of the area of region C to the ratio of the area of region A.

P(B in region C) = area of region C area of region A

Find the probability for the given areas.

area of region A = 24 in2 area of region C = 3 in2

P(B in region C) = ________


Ans

wer

1/8 or 13%

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4 in.

A triangle is inscribed in a square. Point N in the square is selected at random. What is the probability that N lies in the shaded region.

Step 1: Find the area of each region.

area of shaded region = _________ area of square = __________


P(N is in shaded region) = _______________


Using Area to Find Probability

(Answer) / 66

4 in.

A triangle is inscribed in a square. Point N in the square is selected at random. What is the probability that N lies in the shaded region.

Step 1: Find the area of each region.

area of shaded region = _________ area of square = __________


P(N is in shaded region) = _______________




Ans

wer

Follow-up Question :Can you find a shortcut to solve the problem? How would your shortcut make the problem easier? (MP8)- Ans: If you split the square in 1/2 vertically, you can see that the right triangles make up 1/2 of each rectangle. Therefore, the probability for this problem is 1/2.

- Ans: The area of a triangle is the same as the area of a square, except the triangle formula has a 1/2 in front, so the probability of the shaded region is 1/2.

A of shaded = 8 in2

A of square = 16 in2

P(N is in shaded region) = 1/2, 0.5 or 50 %

/ 66

7

16

4

4

Find the probability that a point chosen at random in the trapezoid with a height of 4 will lie in either of the shaded regions.


(Answer) / 66

7

16

4

4

Find the probability that a point chosen at random in the trapezoid with a height of 4 will lie in either of the shaded regions.



Ans

wer

A of shaded= 10 + 8 = 18A of trapezoid = 46

18/46 = 9/23 about 0.39 or 39%

Question on this slide address MP standards:MP2, MP4 & MP5

Additional Q's to help address MP standards:What information are you given? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) Would it help to draw a picture? What would you draw? (MP 4 & MP5)What do you know about 2-d shapes and probability based on area that you can apply to this situation? (MP7)

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16

10

A point in the figure to the right is chosen at random. Find the probability to the nearest percent that the point lies in the shaded region.


(Answer) / 66

16

10




Ans

wer

A of shaded= 40A of entire figure = 160

Probability = 40 = 1 = .25 = 25% 160 4


Additional Q's to help address MP standards:What strategies are you going to use? (MP1) What do you know about 2-d shapes and probability based on area that you can apply to this situation? (MP7)Can you find a shortcut to solve the problem? How would your shortcut make the problem easier? (MP8)- Ans: If you split the rectangle in 1/2 vertically & horizontally, you can see that the shaded right triangles make up 2/8 = 1/4 of the rectangle. Therefore, the probability for this problem is 1/4.

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A point in the figure to the right is chosen at random. Find the probability to the nearest percent that the point lies in the shaded region. 7.07 mm

10 mm


(Answer) / 66

A point in the figure to the right is chosen at random. Find the probability to the nearest percent that the point lies in the shaded region. 7.07 mm

10 mm



Ans

wer

A of shaded= 100 mm2- 50 mm2 = 50 mm2

A of entire figure = 100 mm2

Probability = 50 mm = 1 100 mm 2

= 0.50 = 50 %


Additional Q's to help address MP standards:What strategies are you going to use? (MP1) What do you know about 2-d shapes and probability based on area that you can apply to this situation? (MP7)Can you find a shortcut to solve the problem? How would your shortcut make the problem easier? (MP8)- Ans: If you split the square in 1/2 vertically & horizontally, you can see that the shaded right triangles make up 4/8 = 1/2 of the square. Therefore, the probability for this problem is 1/2.

/ 66

A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region.

12 ft

6 ft


(Answer) / 66

A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region.

12 ft

6 ft



Ans

wer = 61%


Additional Q's to help address MP standards:What information are you given? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) What do you know about 2-D shapes and probability based on area that you can apply to this situation? (MP7)

/ 66

30 cm

50°



(Answer) / 66

30 cm

50°




Ans

wer Question on this slide address MP standards:

MP2, MP4 & MP5

Additional Q's to help address MP standards:What information are you given? (MP1)

What strategies are you going to use? (MP1) What do you know about 2-D shapes and probability based on

area that you can apply to this situation? (MP7)Can you find a shortcut to help you solve this problem? How

does your shortcut make the problem easier? (MP8)- Ans: The shaded region makes up 100 degrees in the circle

& the total degrees are 360, so the probability of the shaded region = 100/360 = 5/18

/ 66

Assume that a dart you throwwill land on the 1-ft square dartboard and isequally likely to land at any point on theboard. Find the probability of hitting each ofthe blue, yellow, and red regions. The radii ofthe concentric circles are 1, 2, and 3 inches,

Using Area to Find Probability - Concentric Circles

P(blue) = P(yellow) = P(red) =

12 in

12 in

(Answer) / 66

Assume that a dart you throwwill land on the 1-ft square dartboard and isequally likely to land at any point on theboard. Find the probability of hitting each ofthe blue, yellow, and red regions. The radii ofthe concentric circles are 1, 2, and 3 inches,


P(blue) = P(yellow) = P(red) =

12 in

12 in


Ans


MP2, MP4 & MP5


/ 66

A point in the figure is chosen at random. Find the probability that the point lies in the shaded region.

3 cm

4 cm2 cm


(Answer) / 66

A point in the figure is chosen at random. Find the probability that the point lies in the shaded region.

3 cm

4 cm2 cm



Ans


MP2, MP4 & MP5


/ 66

A dart is thrown at random at the dart board to the right. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region.

If dimensions are not given, CHOOSE YOUR OWNA good number to use is, An Even Number

HINT:


(Answer) / 66


If dimensions are not given, CHOOSE YOUR OWNA good number to use is, An Even Number

HINT:



Ans

wer



/ 66


This is a square with four semi-circles.

HINT:


(Answer) / 66


This is a square with four semi-circles.

HINT:



Ans

wer



/ 66



(Answer) / 66




Ans

wer

1 = 0.25 = 25%4

Question on this slide address MP standards:

MP2, MP4 & MP5

Additional Q's to help address MP standards:What information are you given? (MP1)What is this problem asking? (MP1)What strategies are you going to use? (MP1) What do you know about 2-d shapes and probability based on area that you can apply to this situation? (MP7)Can you find a shortcut to solve this problem? How would your shortcut make the problem easier? (MP8)- Ans: only 1/4 of the square is shaded, so the probability is 1/4.

/ 66

In the fundraiser game at the right, players toss darts at a board to try to get them into one of the holes. The diameter of the center hole is 8 in. The diameter of each of the four corner holes is 5 in. The board is a 20-in.-by-30-in. rectangle. Find the probability that a tossed dart will go through the indicated hole.

WIN

Dart Toss

a) center hole

b) any corner

c) top right or left

d) bottom left


(Answer) / 66

In the fundraiser game at the right, players toss darts at a board to try to get them into one of the holes. The diameter of the center hole is 8 in. The diameter of each of the four corner holes is 5 in. The board is a 20-in.-by-30-in. rectangle. Find the probability that a tossed dart will go through the indicated hole.

WIN

Dart Toss

a) center hole

b) any corner

c) top right or left

d) bottom left



Ans

wer

/ 66

15 If a dart hits the target at random, what it the probability that it will land in the shaded region?

A 1/3

B 7/16

C 1/9

D 1/4 2 in

6 in

(Answer) / 66

15 If a dart hits the target at random, what it the probability that it will land in the shaded region?

A 1/3

B 7/16

C 1/9

D 1/4 2 in

6 in


Ans

wer

C

/ 66

16 Find the probability that an object falling randomly on the figure will land in the shaded area.

A 0.32

B 0.36

C 0.50

D 0.26

20 in

(Answer) / 66

16 Find the probability that an object falling randomly on the figure will land in the shaded area.

A 0.32

B 0.36

C 0.50

D 0.26

20 in


Ans

wer

A

/ 66

17 What is the probability that a randomly dropped marker will fall in the non-shaded region? A 1/16

B 1/4

C 15/16

D 4

(Answer) / 66

17 What is the probability that a randomly dropped marker will fall in the non-shaded region? A 1/16

B 1/4

C 15/16

D 4


Ans

wer

C

/ 66

18 Two concentric circles have radii of 11 cm and 17 cm. Find the probability to the nearest thousandth that a point chosen at random from the circles is located outside the smaller circle and inside the larger one. A 0.021

B 0.097C 0.581

D 0.647

(Answer) / 66

18 Two concentric circles have radii of 11 cm and 17 cm. Find the probability to the nearest thousandth that a point chosen at random from the circles is located outside the smaller circle and inside the larger one. A 0.021

B 0.097C 0.581

D 0.647 [This object is a pull tab]

Ans

wer

C

/ 66

19 Find the probability that a point chosen at random in the regular triangle lands in the shaded region.

A 25 %

B 30 %

C 33.3 %

D 40 %

3

6

(Answer) / 66

19 Find the probability that a point chosen at random in the regular triangle lands in the shaded region.

A 25 %

B 30 %

C 33.3 %

D 40 %

3

6[This object is a pull tab]

Ans

wer

A

/ 66

8

4

20 Find the probability that a point chosen at random lands in the shaded region. Round to the nearest tenth, if necessary.

A 39.3 %

B 60.7 %

C 64 %

D 36 %

(Answer) / 66

8

4

20 Find the probability that a point chosen at random lands in the shaded region. Round to the nearest tenth, if necessary.

A 39.3 %

B 60.7 %

C 64 %

D 36 %


Ans

wer

B

/ 66

21 Find the probability that a point chosen at random in the circle lands in the shaded region. Round to the nearest tenth.

A 6.9%

B 26.8 %

C 50.0%

D 55.6%

E 27.8%

65°65°

(Answer) / 66

21 Find the probability that a point chosen at random in the circle lands in the shaded region. Round to the nearest tenth.

A 6.9%

B 26.8 %

C 50.0%

D 55.6%

E 27.8%

65°65°


Ans

wer

E

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