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       "Boy, I wish I had some money or game tickets so I could play games. How about you?" asked Sam.

    "I don’t have any cash, but I do have game tickets." said Trey.  "I know! We could play a friendly game for tickets. Then you could trade in your tickets to play games."


Great! Let's play.

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     "That sounds like an idea. What’s the game?" asked Sam.
     "We’ll toss your coin.  I’ll toss first.

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Here are the rules of the game...

Heads, I win.

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Tails, you lose,"
said Trey.
 
"Wait a minute…
that doesn’t sound
like a fair game!
"
said Sam.
"Why not?" asked Trey.
"What makes any game fair?"
Type what makes a game fair in the box.

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"Are you sure it’s not fair?"said Trey. "Let me try."

Trey's FIRST TOSS

Trey's SECOND TOSS

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"It’s tails,
you lose
.

That means I win one ticket.

AG00360_.GIF (6018 bytes) It's heads,
I win

that means I win another ticket."

"How many tickets do you have, Trey?" asked Sam.
 

"How many tickets do you have, Sam?" asked Trey.
 
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"Why, I have two tickets! And you have none." said Trey.

"Now I see what you mean. If we keep this up, you will NEVER have enough tickets to play the arcade games.

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How can we change the game so it is fair?"
Type what you would do to change the
game and make it more fair in the box.

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"Well," said Sam, "for a game to be fair, I should be able to win just as many tosses as you win. That means the probability of tossing heads or tails should be...

wpeA.gif (2128 bytes)     wpeF.gif (2888 bytes)

wpeE.gif (1789 bytes)             wpe10.gif (1785 bytes)

wpeB.gif (2070 bytes)

BS00608_.WMF (7612 bytes)
What do you think?
Is tossing heads more likely?
Is tossing tails more likely?
Is tossing heads or tails equally likely?
Click a button to make a prediction."

Click the arrow to check your prediction.

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Follow the steps to test the prediction...WB01471_.GIF (653 bytes) WB01471_.GIF (653 bytes) WB01471_.GIF (653 bytes) SY00372_.WMF (2666 bytes)

 

 

 



Count the results of tossing
a coin 10 times…
toss2rev.tif (70636 bytes)
How many tails did I toss?  
How many heads did I toss?  
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WB01471_.GIF (653 bytes) WB01471_.GIF (653 bytes) WB01471_.GIF (653 bytes) WB01471_.GIF (653 bytes) SY00373_.WMF (4316 bytes)      Now, let’s put the results on this graph.
                                                      The results were 6 tails, 4 heads.

To graph the results click on one button that matches the results, like this...

wpeB.gif (3418 bytes)


Now the graph
matches the results
of the 10 coin tosses.

The graph we are building is called a Normal Distribution (OR CURVE) Graph. See if you can tell why as we move ahead.

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Now it's your turn to follow the steps...

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Count the results of tossing a coin 10 more times…

wpe5.gif (23238 bytes)

How many tails did I toss?
 

How many heads did I toss?
 


SY00373_.WMF (4316 bytes)     Then add the results to this graph.
I filled in the results from the last ten tosses for you.

wpeB.gif (3418 bytes)

Click one button to add the results of this coin toss to the graph.

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Keep going...

  SY00372_.WMF (2666 bytes)

Count the results of tossing a coin 10 more times…

wpe8.gif (23042 bytes)

How many tails did I toss? 

How many heads did I toss? 


SY00373_.WMF (4316 bytes)      Then add the results to this graph.
We are building this graph as we go. The two colored-in dots show what we have so far.

wpeB.gif (3418 bytes)

Click one button to add the results of this coin toss to the graph.

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Click to show the number of heads and tails for each group of ten coin tosses.
wpe3.gif (23008 bytes)
How many tails?   
How many heads?
wpe6.gif (22217 bytes)
How many tails?   
How many heads?


SY00373_.WMF (4316 bytes) Then add the results to this graph.
Keep building the graph. The colored-in dots show what we have so far.
wpeB.gif (3418 bytes)
Click the buttons to add the results of these two coin tosses to the graph.

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SY00372_.WMF (2666 bytes)
Click to show the number of heads and tails for each group of ten coin tosses one more time!
wpe9.gif (22612 bytes)
How many tails?   
How many heads?
wpe8.gif (23042 bytes)
How many tails?   
How many heads?



SY00373_.WMF (4316 bytes) Then add the results to this graph.
Keep building the graph. The colored-in dots show what we have so far.
wpeB.gif (3418 bytes)
Click the buttons to add the results of these two coin tosses to the graph.

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BS01341_.WMF (19278 bytes)"Wow! It takes many  experiments
to check a prediction,"
said Tray.

So Sam and Trey quickly finished by tossing the coin 10 times in three
different groups.
This chart shows what happened...

3rd ten tosses 4 6
2nd ten tosses 3 7
1st ten tosses 5 5
 Results      tails    heads


SY00373_.WMF (4316 bytes) Add the results from the table to this graph.
wpeB.gif (3418 bytes)
Click the buttons to add the results of the coin tosses to the graph.

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"Now we can see how the results fall on a normal distribution,"
said Sam.

"What in the world is normal distribution?" asked Trey.

"Let’s look at the results on the graph. What do you notice about the data? What is happening?"

 

SL00775_.WMF (4044 bytes)

wpeB.gif (3418 bytes)

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SL00776_.WMF (3070 bytes) "That’s normal distribution!" said Sam. "Do you see how the data are clustered around the center of the graph, just like when you try to hit a target?"


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          wpe2E.gif (842 bytes)          
          wpe2F.gif (842 bytes)          
        wpe2F.gif (842 bytes) wpe2F.gif (842 bytes)          
      wpe2F.gif (842 bytes) wpe2F.gif (842 bytes) wpe2F.gif (842 bytes) wpe2F.gif (842 bytes) wpe2F.gif (842 bytes) wpe2F.gif (842 bytes)    
wpeB.gif (3418 bytes)

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"So now that we know about normal distribution, back to the question...

'Is tossing a coin a fair game?'" asked Sam 

"What makes you think so now?"

Trey said, "I predict you have a fifty-fifty chance of getting heads or tails with a coin toss. But we will need to conduct more experiments to find out for sure.
 

"What we really need to do is change the rules of the game," said Sam. "The rule should be...

"That sounds fair,"
said Trey.

EN00381_.WMF (1300 bytes)Heads,
you
win!

Tails,
            I win!
"

SL01425_.WMF (18798 bytes)

"Now maybe you can win enough tickets to play those games."

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