Title: Lost in Space! Subject: Mathematics · 2006. 6. 9. · Mathematics Grades 5-7 Data Analysis and Probability J. Compute probabilities of compound events, independent events,

Berea City School District Page 1

Title: Lost in Space! Subject: _____Mathematics

Standard: ___Data Analysis and Probability

Grade: ____7 Date: ___April 2006

Vision By the tenth grade Ohio Graduation Test, given the probability of multiple events, the students can organize a sample space and identify the favorable outcomes.

Lesson Summary By the end of this lesson students should be able to compute the probability of compound events using methods as organized lists, tree diagrams, and area models.

Goal(s) of This Lesson Indicator 7D7 Compute probability of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams, and area models.

Prior Knowledge/Pre-Assessment Ratios Fractions Decimals Percents Outcomes of simple events Factor trees Sample space for a single event Vocabulary – outcome, probability, event, frequency table, tally marks, area models, sample space Pre-Assessment options: “Show What You Know” worksheet Probability Connection: Simple Events (4-8)

Team Members Jeanne Binggeli, Ford Gina Ottinger, Ford Valerie Cooper, Ford Julie Yanus, Ford Mary Haffner, Ford Pat Vacca, Ford Kristen Ruggiero, Ford Beverly Sadowski, Ford Melissa Offredo, Roehm Charlene Guzzo, Roehm Peg Keller, Roehm

Reflections/Insights We learned a lot by studying student miscues.


Title: Lost in Space!

Subject: _____Mathematics



Ohio Academic Content Standards Relationship to the Curriculum

Subject Benchmark Indicators A. Use effective listening

strategies, summarize major ideas and draw logical inferences from presentations and visual media.

1. Demonstrate active listening strategies (e.g., asking focused questions, responding to cues, making visual contact).

Language Arts Communication: Oral and Visual 8. Deliver informational presentations that:

a. demonstrate an understanding of the topic and present events or ideas in a logical sequence

K. Make and justify predictions based on experimental and theoretical probabilities.

7. Compute probability of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams, and area models.

Mathematics Grades 5-7

Data Analysis and Probability

J. Compute probabilities of compound events, independent events, and simple dependent events.

Mathematics Grades 8-10

Data Analysis and Probability

B. Analyze and interpret data from scientific investigations using appropriate mathematical skills in order to draw valid conclusions.

7. Use graphs, tables and charts to study physical phenomena and infer mathematical relationships between variables.

Science Scientific Inquiry

Social Studies

Technology






Unit Suggestions Materials and Resources “Show What You Know” – attached; one per student Overhead transparencies or chart paper

• Probability of selecting from NSEW and 1,2,3: Area Model

• Blank Area Model • Probability of selecting from NSEW and 1,2,3: Tree

Diagram and Organized List • Probability of selecting from 3 toppings, 2 sauces

and 3 sizes of pizza: Tree Diagram and Organized List

• Probability of selecting ABCD on two consecutive choices: Area Model

• Probability of selecting ABCD on two consecutive choices: Tree Diagram and Organized List

• Probability of selecting ABCD on three consecutive choices: Tree Diagram and Organized List

Appropriate markers Homework Sheet (one per student) Calculator Possible Pre-Assessments Probability Connection: Simple Events (one per student) “Show What You Know” – attached; one per student

Notes: There are numerous extension activities with answers supplied as attachments to the end of the lesson.

Lesson Plan Suggested

Time Frame and Steps

Teacher Direction, Support and Key Questions Student Learning Activities

Anticipated Student Questions and

Responses Evaluation/ Assessment






8-10 min. 8-15 min.

1. Teacher presents the following problem: There are 4 cards and 3 tiles in a board game. The cards are label N,E,S, and W and the tiles are numbered 1,2 and 3. A player randomly selects one card and one tile. List all of the possible outcomes. Then determine the theoretical probability that you will choose an “S” and a “2”? Teacher observes their work without giving help. 2. Select students to share their work with the class. Discussion of thinking. See if students discover multiplying the two

1. Allow time for independent thinking prior to working in groups. Students then may work with partners or independently. 2. Class members ask clarifying questions. Discussion of thinking.

1. What type of sample space can I use? You may use any type of sample space that will generate the possible outcomes. Incorrect drawings, listings of sample spaces. Students respond with single event answers. Have you listed all of the possible outcomes? Students may add instead of multiply when applying the algorithm for the counting principle. 2. Allow students presenting work to answer questions from other students. Teacher clarifies as

1. Teacher observation 2. See if students discover multiplying the two











8 min.

theoretical probabilities. If not discovered, lead students through the P(S)= 1/4 and P(2)=1/3. Then make the connection by presenting the P(S,2)=1/12. 3. Teacher presents the problem: A customer is ordering a pizza. There are 3 toppings- mushrooms, pepperoni and sausage. There are two types of sauces – red and white. There are three sizes – small, medium and large. What is the theoretical probability this customer ordering a small, red, pepperoni pizza? <OUTCOMES=18> Leading questions:

• What is the probability that a small pizza is ordered? (1/3)

• What is the probability that a red

3. Students then may work with partners or independently. Teacher observes their work without giving help.

necessary. 3. How do you know you found all of the outcomes? Possible student miscues… Students will add instead of multiply. 11/6 (=1/3+1/2+1/3) or 1/8 (1/3+1/2+1/3, improper adding of fractions) or 3/8 (1/3+1/2+1/3, improper adding of fractions)

theoretical probabilities. 3. Each student/ group can demonstrate the use of one or more sample spaces.











12 min. Remainder of class. Allow 10 minutes

pizza is ordered? (1/2)

• What is the probability that a pepperoni pizza is ordered? (1/3)

Write your solution using probability notation. Then change to a decimal and a percent. 4. Teacher presents this problem: You are taking a multiple choice quiz that has 4 choices (A,B,C,D) for each question. What is the theoretical probability that the answers to the first two questions will be choice B? Write your solution in probability notation, then change to a decimal and a percent. 5. Assign homework sheet. Be sure students understand expectations of homework.

4. Students then may work with partners or independently. Teacher observes their work without giving help.

4. How do you know that you found all of the outcomes? 2/8, ¼, 1/8 are all incorrect responses. Anticipate this because students may see only 8 possible outcomes…ABCD for #1 and ABCD for #2. Correct sample space includes 16 possible outcomes.

4. Each student/ group can demonstrate the use of one or more sample spaces.






Differentiated Instructional Support

• Created visual aids on an independent basis as the students’ needs indicated.

• Examine a scantron sheet • Create mental pictures • Use hands-on manipulatives • Additional examples • Simpler problems • Individual rubrics • Leading questions: for example, 1. How would you describe the problem? 2. What facts do you have? 3. Would it help to make a table or draw a

picture? • Different problems for homework which include a

sample problem used as an example.

Extensions See attached sheets: “Probability Extensions”

Technology Connections • www.cbs.com/numbers Great probability lesson as

an extension. Kids play the detective.

Literature Links

http://www.cbs.com/numbers

Assignment

Demonstrate your understanding of the problem by:

1. Listing all of the possible outcomes for this event using at least two of the methods used in class today. Proper labeling is expected.

2. Computing the theoretical probability in fraction, decimal and percent using the list of possible outcomes.

3. Showing the mathematical computation for determining the probability.

A. There are 6 tiles in a bag, 2 yellow, 2 green, and 2 blue. Without looking you will choose one tile, see what color it is, and then replace it. You will then choose a second tile and look at its color. What is the theoretical probability of choosing a blue tile both times?

B. Develop your own theoretical probability problem for your classmates and write it below in

sentence format. Your problem should consist of at least two events. Then demonstrate your understanding of the problem by: 1. Listing all the possible outcomes for this event using at least two of the

methods used in class today. (Proper labeling is expected.) 2. Computing the theoretical probability in fraction, decimal and percent form

using the list of possible outcomes. 3. Showing the mathematical computation for determining the probability.

Berea City School District

Name____________________

Show What You Know

1. You roll a six-sided number cube. a. How many outcomes are possible? b. What is the probability that you will roll a 5? c. How do you write this using probability notation? d. change that to a decimal. e. Change that to a percent. 2. You pick a card from a deck of cards. a. How many outcomes are possible? b. What is the probability that you will roll a 5? c. How do you write this using probability notation? d. change that to a decimal. e. Change that to a percent.



E S W N Choose Card Choose Tile

1 N1 E1 S1 W1

2 N2 E2 S2 W2

N3 E3 S3 W3 3


Card Pick Tile Pick Organized List

#1 N1

N #2 N2

#3 N3

#1 E1

E #2 E2

#3 E3

#1 S1

S #2 S2

#3 S3

#1 W1

W #2 W2

#3 W3


Organized First Second Third

Choice Choice Choice List

Small Mushroom, Red, Small

Red Medium Mushroom, Red, Medium

Large Mushroom, Red, Large

Mushroom

Small Mushroom, White, Small

White Medium Mushroom, White, Medium

Large Mushroom, White, Large

Small Pepperoni, Red, Small

Red Medium Pepperoni, Red, Medium

Large Pepperoni, Red, Large

Pepperoni

Small Pepperoni, White, Small

White Medium Pepperoni, White, Medium

Large Pepperoni, White, Large

Small Sausage, Red, Small

Red Medium Sausage, Red, Medium

Large Sausage, Red, Large

Sausage

Small Sausage, White, Small

White Medium Sausage, White, Medium

Large Sausage, White, Large


A B C D Second Choice

First Choice

A AA AB AC AD

B BA BB BC BD

C CA CB CC CD

D DA DB DC DD


Question 1 Question 2 Organized List

A AA

B AB

A C AC

D AD

A BA

B BB

B C BC

D BD

A CA

B CB

C C CC

D CD

A DA

B DB

D C DC

D DD


Organized Question 1 Question 2 Question 3

Choice Choice Choice List

A

B

A C

D

A

B

B C

D

A

B

C C

D

A

B

D C

D


- - B. D o v ~ l ~ p yaurown iheo~Y.;dpmbabililypmblnn for yowclu8nlatcs end 'hunt* it below.

Thrn ,is, tile oulwmcs idmmpol.,heihconiicaiprobabiiityonihs biickoftbis she",.

El @ @ a

Bmonrtratc your underatanding of the problcm by listing ih~oulmmer in asamplespace wing I oilha 3 methods (lira diagram, beedirgrm, or organid [list) md rnmptlting Uc lllooicfioll problbility of ihc folluumg:

A. 7hucms 6 lilos in a bag, 2 ycilow, 2 grrsn. i d 2 bluc. Wiihout looSngyauwillchooae

tile b~thtirnss? .-

@I

6 b

@I B. Deveiop your o m iheorrtidppmbabilitypmblan T o r ~ u r ~ l u s r n ~ 1 ~ s and iibclaw. Then list ihcoukornss andcom~ntutcihclhcorstical prabsbllity an the back ofthis s h e , .

@I b\ut,wv~b\Si-~i?V' i i ik,abi\hyof-~4\n~@

' I

Fratice Werksheet 4-8 1 Probabilify Connection: Simple Events

I. an e v m nwnbel-

Y6- I 3. a factor of 10 I

I I .,..J 5. B unnpositenumb~l

5 A beg of marbles contains 3 yellow 6 blue 7green 12 whlle, and8 black marbles llyou reach 1;to the beg and brsv one marblealrandom, whaf Is lneprobabflf~y lhnlyou willdraw 3 '6 each of the followIng?Ex~re5~ each rallo as bofh s fml ion anda declmal.c~,,& *7, 7. nydo,v marble 8. e white msrbl~ 0. a biuemarbla (&-To 1

3c-xs;gH~ . w 3 , % .3 . . 3 9 , ,16 XZSG I 10. eitbers bhck or a bluemsrhle 11. ameen, whiZarbluemarble - , ,

A PBCkx98 of candy conlalns Id cherry 16 orange lolemon, and l o llme flavoredcandles llyou i&h lnio thebeckage

l and draw one p m e of candy a1 random what rs the pmbsblllly

I that you WIII draw each afthe follow!ng~ ~xpress each rabo as 1

I

12. s lemon candy $>$ 13.

y .a .- 15. an orange dr lemon o " d y

an orange candy 14. a cherry csndy %5 .32 ?2>0 %g .2% 2.

- ", " .. -='zF %?XZememn, or Werry candy

4'7 .6B ~ f y o P,

18. s candy tbat ia not Lemon, Bme or

Pract?ce Worksheet 4-8

Probability Connection: Simple Events The oplnnerahown el the right lo equally llkeW(n stopon

l each of i r ~ rsgionr numbered l to IS. Flndlhe mbabuity that the splnner wlllslop on essh of ihe fo l low~g.

1. a, , even gum*r 2. a prime number

9-i. &- 3 lb-2-

3. a rGhr of 10 16-7. *. a nunlbpr 11ra than 7

F 3 37

5. a compo.ite ">>mber '' -~,6 F i ' V

A bag otmsrbler conlalos S Y C I ~ W . 6 blue, 7pn,rr, fz whle, ROO 8 blick marber. 11 yo^ roach snto inc ba) sod are* one m~rbbac rana~r r . whaf.rlnrprobabll!ry tlalyou wsl ar3w c3Ch 01 me IOlloxmg? E X p E I ear? raho as bofh B IncbOn 2"" s aw.ma , .*,i /:

7. 0 ye:low marble Ig:yhite r,ahle ablue marble

4%. I:D.,.cw,s, I 3 3 h+?/:b,i6,7%lr 167 %.3$ 10. *,ther a b!.d m a blue ;:a? 11 p a n , whit;, or blue marble

$=&;7 : lg,3gS~,:3Sg &:Z~;~&G~,L,Y~,.G.~L/

A paekqr of u r d y contams 14 chcrry. 15crange. loleron, m d 10 !ma R3vfledcandrr. 11 youreach 1~10 ihrpas~ago ,111dd. .., OOPp<ceorcs-d, Jrr.,ld"m. .r.l,rir ihoprooasllrt" l r l i yo,. *.IIo,.~. racn olrocm. ,* ng? ixorcrs epcn r ~ . o o i DO," a l,c,.on,nd.r <ccln,l,l.,,c/. 7, lz. a iemon candy 18. nn ornngc candy ~ ~ ~ c h e m end7

l L . 1 5iJ- 5,1:5.,ac: i%33~g :q3ac~ ~ p 7 : ~ a-q I \2. l & ~ & ~ ~ ox lamm c"4Y 1 6 a b e lemon, or c h e w candy

SO -a5;13:2$6a'f ~=&,I-I:s,~B%,. GB . sz 17. any c a n e 16. acandythst is not lemm. lime or

Prmeice Worksheet 4-8 i Probability Connection: Simple Evenis me spinner shownat the~lght b equally 11kelyro stop !n esch of 11s regloisnumbered I to 16. Flndlhepmbabllily mar the rplnner will stop on each of the iollowng.

marble af random, what b the piobsbllll lhaf you wllldraw each ofthe lollow!ng? Express each la16 ss bolha lrsction and8 d e c l m a l u 'h 7. s yeUaw mmbia 8. a f i l e marble 9. a blue marble

I - I 12. z

10. ellbw s black or n bluemarble 11. a wn, .rbi* , or t h e m d l e

: 'J A pack.~;c 01.-mjy cmnrans ldcnirry. i60mrg?, lolzmon. and 10 1 .m fla,oredwndes 11 youreach mn tnepad.?ge a lo or 8 , . oocp.e;e of candy at random &vn;rf 8s ihr p,ooablllly ,h.l,,0,8. .so1 ,... r x r i r 01mr ,olox.~?'Expre.i',.,cr r3,oa3 born o t:,o o,, Jrd n d2C mr1'L,,+ % 12. a lemon candy IE@ mom,, candy 14. .a,,

7 G-

16. a&ma, lmon, ar cherry candy

26- 18. n candy that is not lemon, Pme or

Practice worksheet 8-8 Probabiiify Connocfion: Simple Evenfs

\

4. a"um~*?lera *en7

Probability Extensions: a) The teacher puts the names of the 12 girls and 8 boys (all

different) on pieces of paper and then randomly draws a name. She also puts the numbers of the 4 problems to be completed on pieces of paper and randomly draws a paper.

What is the probability that she will draw Sam’s name? 1/20 What is the probability that she will draw problem number 4? 1/4 What is the probability that she will draw Sam’s name and problem #4? Why would you prefer not to go back and do the other methods again? (80 possible outcomes) What is the probability that she will draw a girl’s name? 12/20 or 3/5 What is the probability that she will draw problem number 2? ¼ What is the probability that she will draw a girl’s name and problem number

2? 3/5 x 1/4 = 3/20 What is the probability that she will draw a boy’s name? 8/20 or 2/ 5

What is the probability that she will draw problem number 3 or 4? 2/4 or 1/2

What is the probability that she will draw a boy’s name and problem 3 or 4? 8/20 x 2/4 = 16/80 = 1/5

2/5 x 1/2 = 2/10 = 1/5 b) Find the probability of choosing a green marble at random from

a bag of 3 green and 8 red marbles and then flipping a coin and getting a tail.

3/11 x 1/2 = 3/22 c) Find the probability of rolling a 6 on a number cube and then

rolling a second number cube and getting another 6? 1/6x1/6 = 1/36 Find the probability of rolling a prime number on one number

cube and a composite number on a second number cube? 3/6 x 2/6 = 6/36 d) In the Cafeteria, they decide to save time and bag you lunch.

Yes, it has come to that. No choice. Learn to like what you are served! You will have a ham sandwich, a chicken sandwich or a


hot dog. You will have carrots, celery, broccoli or spinach. Your desert will be apple, cookie, or a banana. If an equal number of each lunch is served what is the probability that your lunch will include a hot dog with carrots and an apple? 1/3 x 1/4 x 1/3 = 1/36

Pick questions from below: Hot dog but no carrots and no apple? 1/3 x 3/4 x 2/3 = 6/36 Hot dog and carrots but no apple? 1/3 x 1/4 x 2/3 = 2/36 Hot dog and no carrots but an apple 1/3 + 3/4 x 1/3 = 3/36 No hot dog and no carrots and no apple? 2/3 x 3/4 x 2/3 = 12/36 No hot dog but carrots but no apple? 2/3 x 1/4 x 2/3 = 4/36 No hot dog and no carrots but an apple 2/3 + 3/4 x 1/3 = 3/36 e) On a multiple choice test (A,B,C,orD), a student does not know

two of the answers and decides to guess. What is the probability that he will be wrong on both questions? 3/4 x 3/4 = 9/16 What is the probability that he will be right on both questions? 1/4 x 1/4 = 1/16 What is the probability that he will be right on one and wrong on the other? 1/4 x 3/4 = 3/16 (right then wrong) 3/4 x 1/4 = 3/16 (wrong then right) 3/16 and 3/16 is 6/16 (Note the sum is 16 for all!) f) Laura has a coin with heads on one side and tails on the other.

She flips it three times. What is the theoretical probability of the coin landing tails up one time and heads up two times?

½ x ½ x ½ = 1/8 H – H – H H – H – T YES H – T – H YES H – T – T T – H – H YES T – H – T T – T – H T – T – T Why do you think your multiplying does not work? Independent vs dependent events: g) What if I picked a number from 1 to 5 out of a hat and did put

the paper back and picked another number? What are the chances of picking a 2 and then a 3?


1/5 x 1/5 = 1/25 = 4% h) What if I picked a number from 1 to 5 out of a hat and did not

put the paper back and picked another number? What are the chances of picking a 2 and then a 3?

1/5 x 1/4 = 1/20 = 5% Did you increase or decease your probability by putting number back --------------------------------------------- i) Jamie has $2 in quarters in his pocket. Three of the quarters

are state quarters. What is the probability that Jamie will draw out a state quarter, put the quarter back and then draw out another state quarter?

3/8 x 3/8 = 9/64 = 0.140625 j) Jamie has $2 in quarters in his pocket. Three of the quarters

are state quarters. What is the probability that Jamie will draw out a state quarter, not put the quarter back and then draw out another state quarter?

3/8 x 2/7 = 6/56 = 0.107142857 Did you increase or decrease your probability by putting the coin back? How is this problem different from the numbers from the hat problem? (Attachments follow that relate to these extensions)



First Choice

Second Choice

Organized List

First Choice

Second Choice

Organized List

Problem 1 G1 #1 Problem 1 B1 #1

Girl 1 Problem 2 G1 #2 Boy 1 Problem 2 B1 #2































Problem 1 G9 #1

Girl 9 Problem 2 G9 #2 Problem 3 G9 #3 Problem 4 G9 #4 Problem 1 G10 #1

Girl 10 Problem 2 G10 #2 Problem 3 G10 #3 Problem 4 G10 #4

Problem 1 G11 #1

Girl 11 Problem 2 G11 #2 Problem 3 G11 #3 Problem 4 G11 #4 Problem 1 G12 #1

Girl 12 Problem 2 G12 #2 Problem 3 G12 #3 Problem 4 G12 #4

Flip Coin

Heads Tails Choose Marble

Green, Heads Green, Tails Green

Green, Heads Green, Tails Green Green, Heads Green, Tails Green

Red, Heads Red, Tails Red Red, Heads Red, Tails Red

Red, Heads Red, Tails Red



Red, Heads Red, Tails Red


First Pick Second Flip Organized List

Heads Green, Heads

Green Tails Green, Tails Heads Green, Heads

Green Tails Green, Tails Heads Green, Heads

Green Tails Green, Tails Heads Red, Heads

Red Tails Red, Tails Heads Red, Heads



Red Tails Red, Tails

Heads Red, Heads




Red Tails Red, Tails


First Roll

Second Roll

OrganizedList

First Second Organized Roll Roll List

1 1,1 1 4,1

2 1,2 2 4,2

1 3 1,3 4 3 4,3

4 1,4 4 4,4

5 1,5 5 4,5

6 1,6 6 4,6

1 2,1 1 5,1

2 2,2 2 5,2

2 3 2,3 5 3 5,3

4 2,4 4 5,4

5 2,5 5 5,5

6 2,6 6 5,6

1 3,1 1 6,1

2 3,2 2 6,2

3 3 3,3 6 3 6,3

4 3,4 4 6,4

5 3,5 5 6,5

6 3,6 6 6,6


Roll Two Roll One

1 2 3 4 5

6

1,1 1,2 1,3 1,4 1,5 1,6 1

2,1 2,2 2,3 2,4 2,5 2,6 2

3,1 3,2 3,3 3,4 3,5 3,6 3

4,1 4,2 4,3 4,4 4,5 4,6 4

5,1 5,2 5,3 5,4 5,5 5,6 5

6,1 6,2 6,3 6,4 6,5 6,6 6


First Roll

Second Roll

OrganizedList

First Second OrganizedRoll Roll List

1 1,1 1 4,1

2 1,2 2 4,2

1 3 1,3 4 3 4,3

4 1,4 4 4,4

5 1,5 5 4,5

6 1,6 6 4,6

1 2,1 1 5,1

2 2,2 2 5,2

2 3 2,3 5 3 5,3

4 2,4 4 5,4

5 2,5 5 5,5

6 2,6 6 5,6

1 3,1 1 6,1

2 3,2 2 6,2

3 3 3,3 6 3 6,3

4 3,4 4 6,4

5 3,5 5 6,5

6 3,6 6 6,6


Organized List Sandwich Vegetable Dessert


Choice Choice Choice Apple Ham, Carrots, Apple

Cookie Ham, Carrots, Cookie Carrots Banana Ham, Carrots, Banana

Apple Cookie

Ham, Celery, Apple Ham, Celery, Cookie

Celery Banana Ham, Celery, Banana

Ham Apple Cookie

Ham, Broccoli, Apple Ham, Broccoli, Cookie

Broccoli Banana Ham, Broccoli, Banana

Apple Cookie

Ham, Spinach, Apple Ham, Spinach, Cookie

Spinach Banana Ham, Spinach, Banana

Apple Cookie

Chicken, Carrots, Apple Chicken, Carrots, Cookie

Carrots Banana Chicken, Carrots, Banana

Apple Cookie

Chicken, Celery, Apple Chicken, Celery, Cookie

Celery Banana Chicken, Celery, Banana

Chicken Apple Cookie

Chicken, Broccoli, Apple Chicken, Broccoli, Cookie

Broccoli Banana Chicken, Broccoli, Banana

Apple Cookie

Chicken, Spinach, Apple Chicken, Spinach, Cookie

Spinach Banana Chicken, Spinach, Banana

Apple Cookie

Hot Dog, Carrots, Apple Hot Dog, Carrots, Cookie

Carrots Banana Hot Dog, Carrots, Banana

Apple Cookie

Hot Dog, Celery, Apple Hot Dog, Celery, Cookie

Celery Banana Hot Dog, Celery, Banana

Hot Dog Apple Cookie

Hot Dog, Broccoli, Apple Hot Dog, Broccoli, Cookie

Broccoli Banana Hot Dog, Broccoli, Banana

Apple Cookie

Hot Dog, Spinach, Apple Hot Dog, Spinach, Cookie

Spinach Banana Hot Dog, Spinach, Banana

Organized First Second Third

Flip Flip Flip List

Heads Heads, Heads, Heads

Heads

Tails Heads, Heads, Tails

Heads

Heads Heads, Tails, Heads

Tails

Tails Heads, Tails, Tails

Heads Tails, Heads, Heads

Heads

Tails Tails, Heads, Tails

Tails

Heads Tails, Tails, Heads

Tails

Tails Tails, Tails, Tails


First Pick First Pick Organized List Replace

#1 1,1 No

#2 1,2 No

#1 #3 1,3 No

#4 1,4 No

#5 1,5 No

#1 2,1 No

#2 2,2 No

#2 #3 2,3 Yes

#4 2,4 No

#5 2,5 No

#1 3,1 No

#2 3,2 No

#3 #3 3,3 No

#4 3,4 No

#5 3,5 No

#1 4,1 No

#2 4,2 No

#4 #3 4,3 No

#4 4,4 No

#5 4,5 No

#1 5,1 No

#2 5,2 No

#5 #3 5,3 No

#4 5,4 No

#5 5,5 No


First Pick First Pick Organized List No Replacement

X x

#2 1,2 No

#1 #3 1,3 No

#4 1,4 No

#5 1,5 No

#1 2,1 No

X x

#2 #3 2,3 Yes

#4 2,4 No

#5 2,5 No

#1 3,1 No

#2 3,2 No

#3 X x

#4 3,4 No

#5 3,5 No

#1 4,1 No

#2 4,2 No

#4 #3 4,3 No

X x

#5 4,5 No

#1 5,1 No

#2 5,2 No

#5 #3 5,3 No

#4 5,4 No

X x


Title: Lost in Space! Subject: Mathematics · 2006. 6. 9. · Mathematics Grades 5-7 Data Analysis and Probability J. Compute probabilities of compound events, independent events,

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