Algebra

Chapter 10B: Probability

Name:______________________________

Teacher:____________________________

Pd: _______

Table of Contents

Chapter 10-5 (Day 1): SWBAT: Determine the experimental probability of an event.

Pgs: 1-5

HW: Pg 6

o Chapter 10-6: (Day 2) SWBAT: Determine the theoretical probability of an event.

Pgs: 7-11

HW: Pg 12

o Chapter 10-6: (Day 3) SWBAT: Calculate Geometric Probability.

Pgs: 13-17

HW: Pgs 18-19

o Chapter 10-7 (Day 4): SWBAT: Calculate the probability of independent and dependent

events. Pgs: 20-24

HW: Pgs 25-26

Chapter 10-8 (Day 5): SWBAT: Construct Tree Diagrams to Determine the Sample Space of All Possible Outcomes

Pgs: 27-35

HW: Pgs 36-37

Chapter 10-8 (Day 6): SWBAT: Solve problems involving permutations.

Pgs: Pgs: 38-42

HW: Pgs 43-45

o Chapter 10 B - Practice Test

Pgs: 46-51

o CHAPTER 10B EXAM: ___/___/2012

1

Chapter 10 - 5 (Day 1)

SWBAT: Determine the experimental probability of an event.

Warm – Up Write the equivalent percent.

1.

2.

3.

4.

An ______________________ is an activity involving chance. Each repetition or observation of an experiment

is a _____________, and each possible result is an ___________________. The ___________________of an

experiment is the set of all possible outcomes.

Example 1: Identifying Sample Spaces and Outcomes

Identify the sample space and the outcome shown for each experiment.

A. Rolling a number cube

B. Spinning a spinner

2

An _____ is an outcome or set of outcomes in an experiment. _________ is the measure

of how likely an event is to occur. Probabilities are written as fractions or decimals from 0 to 1, or as

percents from 0% to 100%.

Example 2: Estimating the Likelihood of an Event

Write impossible, unlikely, as likely as not, likely, or certain to describe each event.

A. A shoe selected from a pair of shoes fits the right foot. ______________________

B. Katrina correctly guesses the last digit of a phone number. ______________________

C. Max pulls a green marble from a bag of all green marbles. ______________________

D. A randomly selected month contains the letter R. ______________________

E. Anthony rolls a number less than 7 on a standard number cube. ______________________

You can estimate the probability of an event by performing an experiment. The ______of an event

is the ratio of the number of times the event occurs to the number of trials. The more trials performed, the more

accurate the estimate will be.

Example 3A: Finding Experimental Probability

An experiment consists of spinning a spinner. Use the results in the table to find the experimental

probability of the event.

F. Spinner lands on orange

G. Spinner does not land on green

3

Practice: Finding Experimental Probability

Practice: Finding Experimental Probability

You Try It!

H.

4

I.

L.

Challenge Problem

5

Summary

Exit Ticket

6

Day 1 - HOMEWORK

7

Chapter 10 – 6 (Day 2)

SWBAT: Determine the theoretical probability of an event.

Warm – Up

When the outcomes in the sample space of an experiment have the same chance of occurring, the

outcomes are said to be ___________________________.

The ______________________________________ of an event is the ratio of the number of ways the event can

occur to the total number of equally likely outcomes.

8

Example 1: Finding Theoretical Probability using a number cube.

An experiment consists of rolling a number cube. Find the theoretical probability of each outcome.

a. P(Rolling an even number) b. P(Rolling a number less than 3)

c. P(Rolling a multiple of 3) d. P(Rolling not a 3)

9

Example 2: Answer each of the following probability problems based on the cards in a standard deck.

10

The ___________________________________ of an event is all the outcomes in the sample space that are not

included in the event. The sum of the probabilities of an event and its complement is 1, or 100%, because the

event will either happen or not happen.

P(event) + P(complement of event) = 1

Example 3: Finding Probability by Using the Complement

Practice: Finding Probability by Using the Complement

1. A jar has green, blue, purple, and white marbles. The probability of choosing a green marble is 0.2, the

probability of choosing blue is 0.3, the probability of choosing purple is 0.1. What is the probability of

choosing white?

2. The weather forecaster predicts a 20% chance of snow. What is the probability that it will not snow?

3. The probability it will rain is 10%. What is the probability it will not rain?

4. The probability of choosing a red marble from a bag is ¾. What is the probability of not choosing a red marble?

11

Challenge SUMMARY Exit Ticket 1. 2.

12

Day 2 - Homework

13

Chapter 10 - 6 (Day 3)

SWBAT: Calculate the Geometric probability

Warm – Up

Find the theoretical probability of each outcome 1. P(rolling a 6 on a number cube)

2. P(picking a Queen from a deck of cards)

Example 1:

14

15

You Try!

16

Problem 2

Challenge

17

I II

IV III

10” 30”

15”

10”

SUMMARY

Exit Ticket

If a dart randomly hits the board, what is the probability that it will hit in region II?

A. 9

20

B. 6

13

C. 1

4

D. 1

3

18

Day 3 - HW

19

3.

4.

20

Chapter 10 - 7 – Day 4

SWBAT: Calculate the probability of independent and dependent events.

Warm – Up

Adam’s teacher gives the class two list of titles and asks each student to choose two of them to

read. Adam can choose one title from each list or two titles from the same list.

21

Events are _______________________________ if the occurrence of one event does not affect

the probability of the other. Events are _____________________________ if the occurrence of

one event does affect the probability of the other.

Example 1: Classifying Events as Independent or Dependent

Tell whether each set of events is independent or dependent. Explain you answer.

A. You select a card from a standard deck of cards and hold it. A friend selects another

card from the same deck.

B. You flip a coin and it lands heads up. You flip the same coin and it lands heads up

again.

Example 2A: Finding the Probability of Independent Events

An experiment consists of randomly selecting a marble from a bag, replacing it, and then

selecting another marble. The bag contains 3 red marbles and 12 green marbles. What is

the probability of selecting a red marble and then a green marble?

Example 2B: Finding the Probability of Independent Events

P ( _____ , ______ ) =

P ( _____ , ______ ) =

22

Practice: An experiment consists of randomly selecting a marble from a bag, replacing

it, and then selecting another marble. The bag contains the following marbles: 3 red, 5

blue, and 2 green.

P(red and green)

P(two reds) P(blue and green)=

P(two greens)

P(red and not red) P(two blues)

An experiment consists of spinning the spinner twice.

P(1 and 6)

P(two 5s) P(even number and 3)=

P(two odd numbers)

P(4 and not 4) P(two 8s)

23

To determine the probability of two dependent events, multiply the probability of

the first event times the probability of the second event after the first event has

occurred.

Practice: Dependent Events Suppose you draw two marbles from a bag containing 6 red, 3 green, 2 yellow, and 4 blue. You

pick the second one without replacing the first one. Find each probability.

P(red and green)

P(two reds) P(yellow and blue)=

P(two greens)

P(red and not red) P(two blues)

Challenge Problem

24

Summary

Exit Ticket

25

Homework

Independent Event (Replacing)

Suppose you have a wardrobe containing 2 blue shirts, 3 yellow shirts and 5 white shirts.

You pick two shirts from the closet replacing the first. Find each probability.

1. P(blue and yellow shirts) =__________

2. P(two yellow shirts) = _________

3. P(yellow and white shirts) =_________

4. P(two white shirts) = _________

An experiment consists of spinning the spinner twice. Find the Probability of each.

5. P(2 and 6) = _________

6. P(two 8s) = _________

7. P(7 and not 7) = _________

8. P(two prime numbers) = _________

26

Dependent Events (without replacing)

Suppose you have a wardrobe containing 2 blue shirts, 3 yellow shirts and 5 white shirts.

Two shirts are picked without replacing the first . Find each probability.

1. P(blue and yellow shirts) =__________

2. P(two yellow shirts) = _________

3. P(yellow and white shirts) =_________

4. P(two blue shirts) = _________

Suppose you draw two cards from a deck of playing cards without replacing the first.

Find each probability.

1. P(spade and diamond) =__________

2. P(two clubs) = _________

3. P(2 of spades and a Jack) =_________

4. P(6 of hearts, and a King) = _________

27

Chapter 10 - 8 (Day 5)

SWBAT: Construct Tree Diagrams to Determine the Sample Space of All Possible Outcomes

Warm – Up

1.

2.

28

Motivation

Mr. Diaz is going to dinner with his family this weekend, so he decides to go shopping with his wife to buy an

outfit. After shopping for several hours, Mr. Diaz and his wife are conflicted. They have to decide on two pairs

of pants, three shirts and two jackets. How many different types of outfits do they have to choose from?

How many outfits can Mr. Diaz Choose from? _________

If Mr. Diaz does not like wearing a striped jacket, how many outfits do not

include a striped jacket? _________

What is the probability of Mr. Diaz choosing Jeans and a white shirt?

29

Example Today your school cafeteria offers:

Main Course Vegetable Pasta Corn

Chicken Mushrooms

Broccoli

If you must choose one vegetable with your main course, (a) Draw a tree diagram to show all the possibilities,

(b) Show a sample space, and (c) How many possibilities are there for lunch?

(d) John does not eat mushrooms. Determine the number of different meals that do not include mushrooms.

(e) John's sister will eat only chicken for her main course. Determine the number of different meals that

include chicken.

(f) What is the probability of a student choosing corn as their vegetable?

30

(a) Draw a tree diagram or create a list of ordered pairs representing all possibilities for who could

be chosen to help with the laundry and with washing the dishes.

(b) Find the probability that both children chosen are girls.

31

Practice Problem # 1

Clayton is flipping three fair coins. Show all the possible outcomes in a tree diagram and answer the following

questions.

Tree Diagram:

Sample Space:

Clayton has three fair coins. Find the probability that he gets two tails and one head when he flips the three coins.

32

Practice Problem # 2

A family had 3 children. Draw a tree diagram to show all the possible Boy/Girl combinations.

Tree Diagram:

Sample Space:

Using your information from above, what is the probability that the family has two boys and one girl?

33

Extension

Suppose the family had another child: How many possible boy/girl combinations are now possible?

The tree could be extended with two new branches from each old branch tip: thus the answer is

_____________________________

This rule is called the ___________________________________________.In many practical situations,

making a tree diagram or listing ordered pairs or triples is not practical.

We can oftentimes shortcut this process by using the Fundamental Counting Principle.

Example 2

Macys offers 5 different types of work shirts, 4 different types of ties, and 3 different types of pants.

How many different shirt/tie/pants combinations are possible?

Practice Problem # 3

A dinner menu lists two soups, seven meats, and three desserts. How many different meals

consisting of one soup, one meat, and one desert are possible? Assume that you cannot repeat

your choice of meat.

Practice Problem # 4

Options on a bicycle include 2 types of handlebars, 2 types of seats, and a choice of 15 colors.

How many possible versions of the bike are possible if a person must chose the handlebars, the seat

and the color?

34

Challenge Problem

• How many different license plates can be formed from the 26 letters of the alphabet and the ten digits

using:

1. 1 letter followed by 4 digits?

2. 3 numbers followed by 3 letters?

3. 4 numbers followed by 3 letters?

SUMMARY

35

Exit Ticket

1.

2.

36

Day 5 - Homework

1. A sandwich can be made with 2 different types of bread, 3 different meats and 3 types of cheese. How many

types of sandwiches can be made if each sandwich consists of one bread, one meat and one type of cheese?

Method 1: Use a tree diagram.

Method 2: Use the Fundamental Counting Principle.

2.

3.

4.

37

5.

6.

38

Chapter 10 - 8 (Day 6)

SWBAT: Solve problems involving permutations.

Warm – Up

REVIEW

________________________________ is used when you need to work with a series of factors, each being one

less than the previous factor.

Instead of writing out 5 · 4 · 3 · 2 · 1, we use factorial notation and write 5! = 120.

(Note: 0! = 1 and 1! = 1)

Example 1: Write out and evaluate each of the following without using your calculator.

a) 6! =

b) (10 - 6)! =

c) 10! =

3! · 2!

39

Practice: Write out and evaluate each of the following without using your calculator.

(a) 2! (b) 3! (c) 4! (d) !4

!8

A ______________________________ is an arrangement of outcomes in which the order does matter.

The order of the arrangement is important!!

For example, show the number of different ways 3 students can enter my classroom.

Example 2: Evaluate each of the following.

How many different ways can 9 people line up for a picture?

Practice: Evaluate each of the following.

a) Noah rented 5 movies. What is the total number ways he can order them to be watched?

b) How many ways are there of rearranging all of the letters in the word MICE?

40

Sometimes we want to permute just a subset of a given set of elements instead of the whole set. This process is

illustrated in the next example.

Example 3: Evaluate each of the following.

Ten people enter a race in which there can be no ties. Different awards are given for first through third

place. In how many different ways can these awards be given out?

Practice: Evaluate each of the following.

a) How many different 3-digit numerals can be made from the digits 4, 5, 6, 7, 8 if a digit can

appear just once in a numeral?

b) How many different 4-letter words can be formed from the letters in the word NUMERAL if there is no

repetition allowed?

c) A coach is trying to pick five players for distinctly different positions on a basketball team. He has 9

players that he can pick from.

41

In general, repetitions are taken care of by dividing the permutation by the number of objects that are identical!

(factorial).

Example 4: Evaluate each of the following.

How many different 5-letter words can be formed from the word APPLE?

Practice: Evaluate each of the following.

a) What is the total number of different four-letter arrangements that can be formed using the letters in the

word "BOOT"?

b) What is the total number of different seven-letter arrangements that can be formed using the letters in

the word "MILLION"?

Challenge All seven-digit telephone numbers in a town begin with 245. How many telephone numbers may be assigned in the

town if the last four digits do not begin or end in a zero?

42

SUMMARY

Exit Ticket

43

Day 6 - Homework

1.

2.

3.

4.

44

5.

The value of 5! is

(1) 1

5 (3) 20

(2) 5 (4) 120

6.

The value of !3

!7 is

(1) 840 (3) 7

(2) 24 (4) 4

7.

Which value is equivalent to ?33 P

(1) 1 (3) 3!

(2) 9 (4) 27

8.

How many different 6-letter arrangements can be formed using the letters in the

word “ABSENT,” if each letter is used only once?

(1) 6 (3) 720

(2) 36 (4) 46,656

9.

How many different 4-letter arrangements can be formed using the letters of the word

“JUMP,” if each letter is used only once?

(1) 24 (3) 12

(2) 16 (4) 4

45

10.

What is the total number of different four-letter arrangements that can be

formed from the letters in the word "VERTICAL," if each letter is used only

once in an arrangement?

(1) 8 (3) 6,720

(2) 1,680 (4) 40,320

11. For problems 1 through 6, find the total number of arrangements of the letters

in the following words. Express your answer in both factorial notation and as

a whole number.

11.

13.

46

Probability Review

Examples: 1) Alex must wear a shirt and tie to work every day.

If he has 5 ties and 3 shirts, determine how many

different ways Alex can wear a shirt and tie?

2) The bowling team at Lincoln High School must

choose a president, vice president, and secretary.

If the team has 10 members, which expression

could be used to determine the number of ways the

officers could be chosen?

(1) 3 10P (3) 10 3P

(2) 7 3P (4) 10 7P

3) Marilyn selects a piece of candy at random from a

jar that contains four peppermint, five cherry,

three butterscotch, and two lemon candies. What

is the probability that the candy she selects is not

a cherry candy?

(1) 0 (3) 9

14

(2) 5

14 (4)

14

14

4) A fair coin is thrown in the air four times. If the

coin lands with the head up on the first three

tosses, what is the probability that the coin will

land with the head up on the fourth toss?

(1) 0 (3) 1

8

(2) 1

16 (4)

1

2

5) A bag of marbles contain 10 red, 4 blue, and 12

green. What is the probability that John picks a

red marble two times in a row, without

replacement?

6) The probability that the Cubs win their first game

is 1

3. The probability that the Cubs win their

second game is 3

7. What is the probability that the

Cubs win both games?

(1) 16

21 (2)

6

7

(3) 1

7 (4)

2

5

47

Directions: Show your work for ALL questions. (if possible)

Finding how many…

1) Max goes through the cafeteria line and counts

seven different meals and three different

desserts that he can choose. Which expression

can be used to determine how many different ways

Max can choose a meal and a dessert?

(1) 7 3 (3) 7 3C

(2) 7 3! ! (4) 7 3P

2) How many different 4-letter arrangements can be

formed using the letters of the word “JUMP,” if

each letter is used only once?

(1) 24 (3) 12

(2) 16 (4) 4

3) Leo purchased five shirts, three pairs of pants, and

four pairs of shoes. Which expression represents

how many different outfits consisting of one shirt,

one pair of pants, and one pair of shoes Leo can

make?

(1) 5 • 3 • 4 (3) 312 C

(2) 5 + 3 + 4 (4) 312 P

4) John is going to line up his four golf trophies on a

shelf in his bedroom. How many different possible

arrangements can he make?

(1) 24 (3) 10

(2) 16 (4) 4

5) How many different outfits consisting of a hat, a

pair of slacks, and a sweater can be made from two

hats, three pairs of slacks, and four sweaters?

(1) 9 (3) 24

(2) 12 (4) 29

6) The school cafeteria offers five sandwich choices,

four desserts, and three beverages. How many

different meals consisting of one sandwich, one

dessert, and one beverage can be ordered?

(1) 1 (3) 3

(2) 12 (4) 60

7) How many different 6-letter arrangements can be

formed using the letters in the word “ABSENT,” if

each letter is used only once?

(1) 6 (3) 720

(2) 36 (4) 46,656

8) Robin has 8 blouses, 6 skirts, and 5 scarves. Which

expression can be used to calculate the number of

different outfits she can choose, if an outfit

consists of a blouse, a skirt, and a scarf?

(1) 8 + 6 + 5 (3) 8! 6! 5!

(2) 8 • 6 • 5 (4) 319 C

9) Show your work!

Paloma has 3 jackets, 6 scarves, and 4 hats.

Determine the number of different outfits

consisting of a jacket, a scarf, and a hat that

Paloma can wear.

10) Show your work!

Six members of a school’s varsity tennis team will

march in a parade. How many different ways can

the players be lined up if Angela, the team captain,

is always at the front of the line?

48

11) Show your work!

There were seven students running in a race. How

many different arrangements of first, second, and

third place are possible?

12) Show Your work!

Debbie goes to a diner famous for its express

lunch menu. The menu has five appetizers, three

soups, seven entrees, six vegetables, and four

desserts. How many different meals consisting of

either an appetizer or a soup, one entree, one

vegetable, and one dessert can Debbie order?

13) Show your work!

Samuel is buying a new car. He wants either a

convertible or a hatchback. Both types of cars are

available in red, white, or blue and with automatic

or standard transmission. Draw a tree diagram or

list a sample space of all possible choices of cars

that are available.

14) Show Your work!

Kimberly has three pair of pants: one black, one

red, and one tan. She also has four shirts: one

pink, one white, one yellow, and one green. Draw a

tree diagram or list the sample space showing all

possible outfits that she could wear, if an outfit

consists of one pair of pants and one shirt. How

many different outfits can Kimberly wear?

49

Experimental and Theoretical Probabilities

15) The graph below shows the hair colors of all the

students in a class.

What is the probability that a student chosen at

random from this class has black hair?

16) The party registration of the voters in Jonesville is

shown in the table below.

If one of the registered Jonesville voters is

selected at random, what is the probability that

the person selected is not a Democrat?

(1) 0.333 (3) 0.600

(2) 0.400 (4) 0.667

17) The faces of a cube are numbered from 1 to 6. If

the cube is rolled once, which outcome is least

likely to occur?

(1) rolling an odd number

(2) rolling an even number

(3) rolling a number less than 6

(4) rolling a number greater than 4

18) A spinner is divided into

eight equal regions as shown

in the diagram below.

Which event is most likely

to occur in one spin?

(1) The arrow will land in a green or white area.

(2) The arrow will land in a green or black area.

(3) The arrow will land in a yellow or black area.

(4) The arrow will land in a yellow or green area.

19) The faces of a cube are numbered from 1 to 6.

What is the probability of not rolling a 5 on a single

toss of this cube?

(1) 6

1 (3)

5

1

(2) 6

5 (4)

5

4

20) If the probability that it will rain on Thursday is 5

6, what is the probability that it will not rain on

Thursday?

(1) 1 (3) 1

6

(2) 0 (4) 5

6

50

21) If the probability of a spinner landing on red in a

game is 1

5, what is the probability of it not landing

on red?

(1) 20% (3) 50%

(2) 25% (4) 80%

22) A box contains 6 dimes, 8 nickels, 12 pennies, and 3

quarters. What is the probability that a coin drawn

at random is not a dime?

(1) 6

29 (3)

12

29

(2) 8

29 (4)

23

29

23) A six-sided number cube has faces with the

numbers 1 through 6 marked on it. What is the

probability that a number less than 3 will occur on

one toss of the number cube?

(1) 1

6 (3)

3

6

(2) 2

6 (4)

4

6

24) A box contains six black balls and four white balls.

What is the probability of selecting a black ball at

random from the box?

(1) 1

10 (3)

4

6

(2) 6

10 (4)

6

4

25) Seth tossed a fair coin five times and got five

heads. The probability that the next toss will be a

tail is

(1) 0 (3) 6

5

(2) 6

1 (4)

2

1

26) As captain of his football team, Jamal gets to call

heads or tails for the toss of a fair coin at the

beginning of each game. At the last three games,

the coin has landed with heads up. What is the

probability that the coin will land with heads up at

the next game? Explain your answer.

51

Independent and Dependent Probabilities

27) Bob and Laquisha have volunteered to serve on the

Junior Prom Committee. The names of twenty

volunteers, including Bob and Laquisha, are put into

a bowl. If two names are randomly drawn from the

bowl without replacement, what is the probability

that Bob’s name will be drawn first and Laquisha’s

name will be drawn second?

(1) 20

1

20

1 (3)

2

20

(2) 19

1

20

1 (4)

2

20!

28) Brianna is using the two spinners shown below to

play her new board game. She spins the arrow on

each spinner once. Brianna uses the first spinner

to determine how many spaces to move. She uses

the second spinner to determine whether her move

from the first spinner will be forward or backward.

Find the probability that Brianna will move fewer than four spaces and backward.

29) The probability that Jinelle’s bus is on time is

2

3,

and the probability that Mr. Corney is driving the

bus is 4

5. What is the probability that on any

given day Jinelle’s bus is on time and Mr. Corney is

the driver?

(1) 2

15 (3)

10

12

(2) 8

15 (4)

6

8

30) A student council has seven officers, of which five

are girls and two are boys. If two officers are

chosen at random to attend a meeting with the

principal, what is the probability that the first

officer chosen is a girl and the second is a boy?

(1) 10

42 (3)

7

14

(2) 2

7 (4)

7

13

31) Selena and Tracey play on a softball team. Selena

has 8 hits out of 20 times at bat, and Tracey has 6

hits out of 16 times at bat. Based on their past

performance, what is the probability that both

girls will get a hit next time at bat?

(1) 1 (3) 31

40

(2) 14

36 (4)

48

320

32) Show all work!

Mr. Yee has 10 boys and 15 girls in his mathematics

class. If he chooses two students at random to

work on the blackboard, what is the probability

that both students chosen are girls?