NAME DATE PERIOD Lesson 1 Reteachngillncs.weebly.com/uploads/2/7/1/1/27117493/packet.pdf · 2019-08-16 · Probability of Simple Events When tossing a coin, there are two possible

Course 2 • Chapter 9 Probability 137

NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 1 ReteachProbability of Simple Events

When tossing a coin, there are two possible outcomes, heads and tails. Suppose you are looking for heads. If the coin lands on heads, this would be a favorable outcome. The chance that some event will happen (in this case, getting heads) is called probability. You can use a ratio to fi nd probability.The probability of an event is a number from 0 to 1, including 0 and 1. The closer a probability is to 1, the more likely it is to happen.

Example 1There are four equally likely outcomes on the spinner.Find the probability of spinning green or blue.

P(green or blue) = number of favorable outcomes −−−−−−−−−−−−−−−−

number of total outcomes

= 2 −

4 or 1 −

2

The probability of landing on green or blue is 1 −

2 , 0.50, or 50%.

Complementary events are two events in which either one or the other must happen, but bothcannot happen at the same time. The sum of the probabilities of complementary events is 1.

Example 2There is a 25% chance that Sam will win a prize. What is the probabilitythat Sam will not win a prize?

P(win) + P(not win) = 1

0.25 + P(not win) = 1 -0.25 = -0.25

P(not win) = 0.75

So, the probability that Sam won’t win a prize is 0.75, 75%, or 3 −

4 .

Exercises

1. There is a 90% chance that it will rain. What is the probability that it will not rain?

One pen is chosen without looking from a bag that has 3 blue pens, 6 red, and 3 green. Find the probability of each event. Write each answer as a fraction, a decimal, and a percent.

2. P(green) 3. P(blue or red) 4. P(not red)

75% 100%50%25%0%

10 14 or 0.25 1

2or 0.50 3

4or 0.75

impossible to occur equally likely to occur certain to occur

blue

yellow

red

green

137_152_CC_A_RSPC2_C09_662331.indd Page 137 7/21/11 8:00 AM s-60user137_152_CC_A_RSPC2_C09_662331.indd Page 137 7/21/11 8:00 AM s-60user /Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/.../Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/...

PDF Pass

138 Course 2 • Chapter 9 Probability

NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com

panies, Inc. Permission is granted to reproduce for classroom

use.Lesson 1 Skills PracticeProbability of Simple Events

OR

Q

BAS

EK

dog

cat

catdog

hamster

dog

A card is randomly chosen. Find each probability. Write each answer as a fraction, a decimal, and a percent.

1. P(B)

2. P(Q or R)

3. P(vowel)

4. P(consonant or vowel)

5. P(consonant or A)

6. P(T)

The spinner shown is spun once. Write a sentence explaining how likely it is for each event to occur.

7. P(dog)

8. P(hamster)

9. P(dog or cat)

10. P(bird)

11. P(mammal)

WEATHER The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.

12. What is the probability that it will not be windy?

13. Will tomorrow be a good day to fly a kite? Explain.


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 2 ReteachTheoretical and Experimental Probability

Example 1The graph shows the results of an experiment in which a number cube was rolled 100 times.Find the experimental probability of rolling a 3 for this experiment. Then compare it to the theoretical probability.

P(3) =

number of times 3 occurs −−−−−−−−−−−−−−−−−

number of possible outcomes

= 16 −−−

100 or 4 −−

25

The experimental probability of rolling a 3 is 4 −−

25 , which

is close to its theoretical probability of 1 −

6 .

Example 2In a telephone poll, 225 people were asked forwhom they planned to vote in the race for mayor.What is the experimental probability of Juarez getting a vote from a person selected at random?

Of the 225 people polled, 75 planned to vote for Juarez.

So, the experimental probability is 75 −−−

225 or 1 −

3 .

Example 3Suppose 5,700 people vote in the election. How many can be expected tovote for Juarez?

1 −

3 · 5,700 = 1,900

About 1,900 will vote for Juarez.

Exercises

1. PETS Use the graph of a survey of 150 students asked whether they prefer cats or dogs.

a. What is the experimental probability of a student preferring dogs?

b. Suppose 100 students were surveyed. How many can be expected to prefer dogs?

c. Suppose 300 students were surveyed. How many can be expected to prefer cats?

Experimental probability is found using frequencies obtained in an experiment or game. Theoretical

probability is the expected probability of an event occurring.

6321

20

10

15

25

0

5Num

ber o

f Rol

ls

54

14 1316

1921

17

Number Showing

Number Cube Experiment

Candidates Number of People

Juarez 75Davis 67Abramson 83

DogsCats

60

80

100

40

0

20

120

140

Num

ber o

f Stu

dent

s

Pet Preferences

18

132


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com


use.

1. A number cube is rolled 50 times and the results are shown in the graph below.

6321

8

10

12

4

6

14

0

2

Num

ber o

f Rol

ls

Number Cube Experiment

Number Showing54

108

6

9

5

12

a. Find the experimental probability of rolling a 2.

b. What is the theoretical probability of rolling a 2?

c. Find the experimental probability of not rolling a 2.

d. What is the theoretical probability of not rolling a 2?

e. Find the experimental probability of rolling a 1.

2. SEASONS Use the results of the survey at

Spring

Summer

Fall

Winter

None, I likethem all

13%

39%

25%

13%

10%

What is Your FavoriteSeason of the Year?the right.

a. What is the experimental probability that a person’s favorite season is fall? Write the probability as a fraction.

b. Out of 300 people, how many would you expect to say that fall is their favorite season?

c. Out of 20 people, how many would you expect to say that they like all the seasons?

d. Out of 650 people, how many more would you expect to say that they like summer more than they like winter?

Lesson 2 Skills PracticeTheoretical and Experimental Probability


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 3 ReteachProbability of Compound Events

A tree diagram or table is used to show all of the possible outcomes, or sample space, in a probability experiment.

Example 1WATCHES A certain type of watch comes in brown or black and in a small orlarge size. Find the number of color-size combinations that are possible.

Make a tree diagram to show the sample space. Then give the total number of outcomes.

BrownSmall

Large Brown, Large

Color Size Sample Space

BlackSmall

Large

Black, Small

Brown, Small

Black, Large

There are four different color and size combinations.

Example 2CHILDREN The chance of having either a boy or a girl is 50%. What is the probability of the Smiths having two girls?

Make a tree diagram to show the sample space. Then find the probability of having two girls.

boyboy

girl boy, girl

Child 1 Child 2 Sample Space

girlboy

girl

girl, boy

boy, boy

girl, girl

The sample space contains 4 possible outcomes. Only 1 outcome has both children being girls. So, the probability of the Smiths having two girls is 1 −

4 .

ExercisesFor each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.

1. choosing an outfit from a green shirt, blue shirt, or a red shirt, and black pants or blue pants

2. choosing a vowel from the word COUNTING and a consonant from the word PRIME


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 3 Homework PracticeProbability of Compound Events

For each situation, find the sample space using a tree diagram.

1. choosing blue, green, or yellow wall paint with white, beige, or gray curtains

2. choosing a lunch consisting of a soup, salad, and sandwich from the menu shown in the table

Soup Salad Sandwich

Tortellini Caesar Roast Beef

Lentil Macaroni Ham

Turkey

3. GAME Kimiko and Miko are playing a game in which each girl rolls a number cube. If the sum of the numbers is a prime number, then Miko wins. Otherwise Kimiko wins. Find the sample space. Then determine whether the game is fair.

Sum = 2 Sum = 3 Sum = 4 Sum = 5 Sum = 6 Sum = 7 Sum = 8 Sum = 9 Sum = 10 Sum = 11 Sum = 12

1 + 1 = 22 + 1 = 3

1 + 2 = 3

1 + 3 = 4

2 + 2 = 4

3 + 1 = 4

1 + 4 = 5

2 + 3 = 5

3 + 2 = 5

4 + 1 = 5

1 + 5 = 6

2 + 4 = 6

3 + 3 = 6

4 + 2 = 6

5 + 1 = 6

1 + 6 = 7

2 + 5 = 7

3 + 4 = 7

4 + 3 = 7

5 + 2 = 7

6 + 1 = 7

2 + 6 = 8

3 + 5 = 8

4 + 4 = 8

5 + 3 = 8

6 + 2 = 8

3 + 6 = 9

4 + 5 = 9

5 + 4 = 9

6 + 3 = 9

4 + 6 = 10

5 + 5 = 10

6 + 4 = 10

5 + 6 = 11

6 + 5 = 116 + 6 = 12

137_152_CC_A_HWPSC2_C09_662334.indd Page 141 28/07/11 7:37 AM s-60user137_152_CC_A_HWPSC2_C09_662334.indd Page 141 28/07/11 7:37 AM s-60userVolumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURSE1-3..Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURS

PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 5 ReteachFundamental Counting Principle

Example CLOTHING Andy has 5 shirts, 3 pairs of pants, and 6 pairs of socks. How many different outfits can Andy choose with a shirt, pair of pants, and pair of socks?

number of pairs number of shirts number of pants of socks total number of outfi ts

5 3 6 = 90

Andy can choose 90 different outfits.

ExercisesUse the Fundamental Counting Principle to find the total number of outcomes in each situation.

1. rolling two number cubes

2. tossing 3 coins

3. picking one consonant and one vowel

4. choosing one of 3 processor speeds, 2 sizes of memory, and 4 sizes of hard drive

5. choosing a 4-, 6-, or 8-cylinder engine and 2- or 4-wheel drive

6. rolling 2 number cubes and tossing 2 coins

7. choosing a color from 4 colors and a whole number from 4 to 10

If event M can occur in m ways and is followed by event N that can occur in n ways, then the event M followed by N can occur in m × n ways. This is called the Fundamental Counting Principle.

· ·

⎧

�

⎨

�

⎩

⎧

�

⎨

�

⎩

⎧

�

⎨

�

⎩

⎧

�

⎨

�

⎩


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com


use.Lesson 5 Skills PracticeFundamental Counting Principle

Use the Fundamental Counting Principle to find the total number of outcomes in each situation.

1. rolling two number cubes and tossing one coin

2. choosing rye or Bermuda grass and 3 different mixtures of fertilizer

3. making a sandwich with ham, turkey, or roast beef; Swiss or provolone cheese; and mustard or mayonnaise

4. tossing 4 coins

5. choosing from 3 sizes of bottled water and from distilled, filtered, or spring water

6. choosing from 3 flavors and 3 sizes of juice

7. choosing from 35 flavors of ice cream; one, two, or three scoops; and sugar or waffle cone

8. picking a day of the week and a date in the month of April

9. rolling 3 number cubes and tossing 2 coins

10. choosing a 4-letter password using only 5 letters that may each be used more than once

11. choosing a bicycle with or without shock absorbers; with or without lights; and 5 color choices

12. a license plate that has 3 numbers from 0 to 9 and 2 letters where each number and a letter may be used more than once


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 6 ReteachPermutations

Example 1BOOKS How many ways can 4 different books be arranged on a bookshelf?

This is a permutation. Suppose the books are placed on the shelf from left to right.

There are 4 choices for the fi rst book.

There are 3 choices that remain for the second book.

There are 2 choices that remain for the third book.

There is 1 choice that remains for the fourth book.

4 · 3 · 2 · 1 = 24 Simplify.

So, there are 24 ways to arrange 4 different books on a bookshelf.

Example 1Find P(5,4).

P(5, 4) P(5,4) = 5 5 · 4 · 3 · 2 or 120 Simplify.

ExercisesFind each value. Use a calculator if needed.

1. P(3,2) 2. P(7,6)

3. P(6,3) 4. P(9,3)

5. How many ways can you arrange the letters in the word group?

6. How many different 4-digit numbers can be created if no digit can be repeated? Remember, a number cannot begin with 0.

A permutation is an arrangement, or listing, of objects in which order is important. You can use the Fundamental Counting Principle to fi nd the number of possible arrangements.


PDF Pass

PermutationsProbability Word Problems

Name: Date:

Copyright ©2014 WorksheetWorks.com

( 1 ) Mark has a collection of 7 toy train

cars and creates a train using 4 of

them. How many different ways could

he have made the train?

( 2 ) How many different ways can Emma,

Rachel, Steven, Aaron, Timothy and

Amanda stand in a row?

( 3 ) How many 3-letter sequences can be

made from the letters in the word

IMPEACH?

( 4 ) In a 7-person race, how many

different ways can the runners arrive

at the finish line?

( 5 ) 5 people walk into a fast-food

restaurant at the same time. How

many different ways can the first 3 be

served?

( 6 ) Emma was asked to choose 3

paintings from a collection of 8 and

hang them on the wall in a row. How

many different ways could the wall be

decorated?


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 7 ReteachIndependent and Dependent Events

The probability of two independent events can be found by multiplying the probability of the fi rst event by the probability of the second event.

Example 1Two number cubes, one red and one blue, are rolled. What is the probability that the outcome of the red number cube is even and the outcome of the blue number cube is a 5?

P(red number cube is even) = 1 −

2

P(blue number cube is a 5) = 1 −

6

P(red number cube is even and blue number cube is a 5) = 1 −

2 · 1 −

6 or 1 −−

12

The probability that the two events will occur is 1 −−

12 .

Example 2There are 6 black socks and 4 white socks in a drawer. If one sock is taken out without looking and then a second is taken out, what is the probability that they both will be black?

P(first sock is black) = 6 −−

10 or 3 −

5 6 is the number of black socks; 10 is the total number of socks.

P(second sock is black) = 5 −

9 5 is the number of black socks after one black sock is removed; 9 is the

total number of socks after one black sock is removed.

P(two black socks) = 3 −

5 · 5 −

9 or 1 −

3

The probability of choosing two black socks is 1 −

3 .

ExercisesA card is drawn from a deck of 10 cards numbered 1 through 10 and a number cube is rolled. Find each probability.

1. P(10 and 3) 2. P(two even numbers)

3. P(two prime numbers) 4. P(9 and an odd number)

5. P(two numbers less than 4) 6. P(two numbers greater than 5)

There are 4 red, 6 green, and 5 yellow pencils in a jar. Once a pencil is selected, it is not replaced. Find each probability.

7. P(red and then yellow) 8. P(two green)

9. P(green and then yellow) 10. P(red and then green)

If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs.


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com


use.Lesson 7 Skills PracticeIndependent and Dependent Events

For Exercises 1–6, a number cube is rolled and the spinner at the right is spun. Find each probability.

1. P(1 and A) 2. P(odd and B)

3. P(prime and D) 4. P(greater than 4 and C)

5. P(less than 3 and 6. P(prime and consonant)

consonant)

7. What is the probability of spinning the spinner above 3 times and getting a vowel each time?

8. What is the probability of rolling a number cube 3 times and getting a number less than 3 each time?

Each spinner at the right is spun. Find each probability.

9. P(A and 2)

10. P(vowel and even)

11. P(consonant and 1)

12. P(D and greater than 1)

There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find each probability.

13. P(red and then yellow) 14. P(blue and then yellow)

15. P(red and then blue) 16. P(two yellow marbles)

17. P(two red marbles in a row) 18. P(three red marbles)

GAMES There are 13 yellow cards, 6 blue, 10 red, and 8 green cards in a stack of cards turned face down. Once a card is selected, it is not replaced. Find each probability.

19. P(2 blue cards) 20. P(2 red cards)

21. P(a yellow card and 22. P(a blue card and then a green card) then a red card)

23. P(two cards that are not red) 24. P(two cards that are neither red or green)


PDF Pass

Documents

NAME DATE PERIOD Lesson 1 Reteachngillncs.weebly.com/uploads/2/7/1/1/27117493/packet.pdf · 2019-08-16 · Probability of Simple Events When tossing a coin, there are two possible