Last time we met, we started an experiment.  Here we are again to figure out how many boys and girls are coming to my party using a tree diagram
Let's see if you remember what a tree diagram is.
    A tree diagram
is a picture of a tree
shows the possible combinations or outcomes of an event on its branches so you can predict events
looks the same every time
can solve problems
Click to choose your answer, then click on the pictures to check.


 



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So far, we have this tree diagram to show our possible outcomes and to help us predict. 
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Click on the arrows to choose the answers to the questions.

How many possible outcomes are there for John?   
How many possible outcomes are there for Josť?  
How many possible outcomes will Rosa and Amal have together if they follow the same pattern?  
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What are Rosa's possible outcomes? Fill in this table using the pattern on the tree diagram.
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Click on the picture to go back to the tree diagram.

Rosa's Table of Possible Outcomes Click each arrow to choose.
1st in pair, 2nd in pair

First Friend,

Second Friend

boy,

girl

Joe (boy),

Amy (girl)

boy,

Joe (boy),

(girl)

boy,

(boy),

(boy)

girl,

girl

(girl),

(girl)

girl,

boy

(girl),

Juan (boy)  

girl,

Lili (girl)

Juan (boy)

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Now our tree diagram looks like this. Rosa's branch of the tree diagram is colored pink.
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PE02286_.WMF (30492 bytes) It's almost like magic, but our possible outcomes are following a pattern.
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Our tree diagram is almost complete.
How many outcomes will Amal have if she follows the same pattern as her friends?
 
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Click to show the possible outcomes for Amal. Click on the picture to check.

Girls Boys
Ana Kay Bo T.J.
Ana Kay Bo T.J.
Ana Kay Bo T.J.
Ana Kay Bo T.J.
Ana Kay Bo T.J.
Ana Kay Bo T.J.

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Now our tree diagram shows all of the possible outcomes. It shows four branches of our tree diagram.
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How many possible outcomes are there?  Use the tree diagram and then type your answer in the box.

 

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Did you use the tree diagram to solve the problem?wpe7.jpg (15502 bytes)

SO01561_.WMF (23000 bytes) How did you figure out the total number of possible outcomes?
Type your answer in the box.

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Now we know all of the possible outcomes. The group of possible outcomes is called the sample space.
What is our sample space?            SO00391_.WMF (2088 bytes)
The total number of presents I will get at my party.
The total number of boys and girls coming to my party.
The total number of possible outcomes on the tree diagram.
The total number of people coming to the party.
Click on the piece of cake to check your answer.

Click on the picture to see the sample space on the tree diagram.
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There are so many possible outcomes. How can we narrow them down?

I know, we can look at only one event.
Which event would you like to predict?

The event of only boys coming to the party.
How many possible outcomes are there for this event?
The event of only girls coming to the party.
How many possible outcomes are there for this event?
Click on your choice.

Is blowing out the candles on the cake an event?
No, blowing out the candles is not an event in our experiment.

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Now let's find all of the outcomes on the tree diagram that match the event you chose.
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How many possible outcomes are there for this event on the tree diagram?
...
only boys coming to the party?
 
...only girls coming to the party?

 
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The pink shows only girls coming to the party.
The green shows
only boys coming
to the party.
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Follow the branches on the tree diagram
to find...
How many possible outcomes show
an equal number of boys and girls
coming to the party?

 

 

 

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Let's chart what we know so far.
Click on the arrows to show what you know and to make predictions about events you are unsure about.
Event
___________________________________
Number of Outcomes
Only boys coming to the party
Only girls coming to the party
An equal number of girls and boys coming to the party
More boys than girls coming to the party
More girls than boys coming to the party


Click on the picture to go back to the tree diagram.
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Check your predictions with this tree diagram.wpe5.jpg (15722 bytes)
KEY :    Green = Only boys       Pink = Only girls
   Purple = More boys than girls  Red = More girls than boys




Use the tree diagram to help you predict which of these events is most likely...
only boys
only girls
an equal number of girls and boys
more boys than girls
more girls than boys
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Now you have used tree diagrams to show possible outcomes and predict events. You helped me figure out how many girls or boys might come to my party.

In the real world, people use tree diagrams every day to solve problems too. 
How do people solve problems using tree diagrams?
Click in the box for your choice, then on the text for hints.
To decide what to do with their money
To build things, like structures and systems
To design things, like experiments and models
To recognize patterns in cycles and data


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Click on the picture to check your answers.

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