Math 7

Unit 7 Data Analysis

Lesson 7.6  Tree Diagrams

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

Investigate outcomes of probability experiments.

There isn’t a Focus activity in this lesson.

TEXT Page 284

Read/Work through the  Focus  section at the top of page 284 in  your textbook.

Explore

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

TEXT Page 284

Read/Work through the  Explore  section on Page BLAH in your textbook.

You can do this activity on your own.
Do your best to answer the questions, then watch the Video Tutorial for help or to check your answers.

I encourage you to do this experiment “for real”,  roll a die and flip a coin.
Doing it 100 times would be a stretch, but that is what the textbook is asking you to do...

If you like, you can use the simulation below to do the experiment.

Coin Die Simulation

dicelist={{Disk[{0,0},0.2]},{Disk[{0.6,0.6},0.2],Disk[{-0.6,-0.6},0.2]},{Disk[{0,0},0.2],Disk[{0.6,0.6},0.2],Disk[{-0.6,-0.6},0.2]},{Disk[{0.6,0.6},0.2],Disk[{-0.6,-0.6},0.2],Disk[{0.6,-0.6},0.2],Disk[{-0.6,0.6},0.2]},{Disk[{0,0},0.2],Disk[{0.6,0.6},0.2],Disk[{-0.6,-0.6},0.2],Disk[{0.6,-0.6},0.2],Disk[{-0.6,0.6},0.2]},{Disk[{-0.6,0},0.2],Disk[{0.6,0},0.2],Disk[{0.6,0.6},0.2],Disk[{-0.6,-0.6},0.2],Disk[{0.6,-0.6},0.2],Disk[{-0.6,0.6},0.2]}};

Dice[i_]:=Graphics[{{White,EdgeForm[Directive[Black,Thickness[0.045]]],Rectangle[{-1,-1},{1,1}]},Part[dicelist,i]},ImageSize->50];


penny["head"]=; penny["tail"]=;

Manipulate[
Column[{
Row[{penny[n1], Dice[n2]}],
Button["New trial", (n1 =RandomChoice[{"head", "tail"}]; n2=  RandomInteger[{1,6}])]
}], {{n1,"head", "Coin"}, {"head", "tail"},ControlType->SetterBar}, {{n2,2, "Dice"}, 1, 6,1,ControlType->SetterBar},SaveDefinitions->True]

Conducting multiple trials  (I changed this back to 6000 ,  too many trials slowed the file down too much)

outcomelist=Tuples[{{"H", "T"}, Range[6]}];
list =Table[{RandomChoice[{"H", "T"}], RandomInteger[{1,6}]}, {i, 1, 6000}];
Manipulate[
BarChart[
Length[Cases[Take[list, n], #]]&/@outcomelist,ChartLabels->{"H1","H2","H3","H4","H5","H6","T1","T2","T3","T4","T5","T6"}], {{n, 1,"Number of trials"},1 ,6000,1,Appearance->"Labeled"}, SaveDefinitions->True]

Watch

Video Tutorial

Video Tutorial   (Computer)

Connect

Connect summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 285

Read/Work through the  Connect  section on Page 285 in your textbook.

Example

The Example will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example

TEXT Pages 285 - 286

Work through the Example on Pages 285 - 286  in your textbook.

Watch

Video Tutorial

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Assessment Focus a question that gives a good example of the kind of question you would be expected to answer after completing the lesson

Take It Further questions offer enrichment and extension.

Notes

Question 7,   I didn’t go through and do the experiment, so in this one I just calculate the THEORETICAL probability.
The more often you actually do the experiment, the closer the experimental probability will get to the theoretical probability.

Below,  a pre-run set of trials,  100 of them,  if you want to “sort of” do the experiment.

outcomelist=Tuples[{{"green", "red", "yellow", "blue"}, Range[8]}];
list =Table[{RandomChoice[{"green", "red", "yellow", "blue"}], RandomInteger[{1,8}]}, {i, 1, 100}];

Manipulate[
Row[list[[n1]]],
{{n1,1, "trial number"}, 1,100,1} ,SaveDefinitions->True]

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", , , }})