Now that we are at the party, it’s time to play a game. At the same time, we can learn about...

probability.

"What

is

probability?"

SL00722_.WMF (8460 bytes)


PE03544_.WMF (3016 bytes)I will help you learn all about probability.
What do you think probability is?

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Probability is a part of math that
predicts the chance or likelihood that something may or may not happen.
Mathematicians put that into a number like...

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There is a 20% chance of rain today.

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The ratio of a nickel to a dime is 2 : 1.

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The odds are 20 to 1 we will win the game.

This helps us make decisions and predict what is going to happen
without just guessing.

 
Where have you heard about
probability?
PE03563_.WMF (4380 bytes)Probability looks at
the chances of an event
happening or not happening.
"Will I hit the ball or not?"

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Probability is everywhere, but my game,

AN03572_1.WMF (14212 bytes) Pin the Tail
on the Tiger

can help us see how probability works.

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Okay,
who goes first?

If we put these numbers in a bag...
wpeA.gif (3860 bytes)

Well, probability can help us figure that out too.

What is the likelihood of drawing a
1, 2, 3, 4, 5, or 6 out of the bag?

What is the likelihood of drawing the number zero out of the bag?  Previous Page |  Next Page








 

We can turn the likelihood into a number probability
by using the...

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Look at the Number Line to answer the questions.

It’s time to draw your number from the bag.

What is the probability you will draw
a zero from the bag?
 
What is the probability you will draw
either a 1, 2, 3, 4, 5, or 6 from the bag?
 

AG00081_.GIF (10442 bytes)

Did you pick your
number for the game?

What number did you pick?


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Now we are ready to play the game. How do we play? 

Well, it’s like

"Pin the Tail on the Donkey."

AN01366_.WMF (9364 bytes)

EN00323_.WMF (1800 bytes)Instead of walking so many steps and then placing the tail on the donkey, we will roll one die.    



What do you know about dice?
How do you use dice?

"Why are we going to roll a die in this game?"

That brings us back to probability.PE03549_.WMF (5442 bytes)

Probability
looks at
all of the possibilities.

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We are going to use a
standard die
in our game to see how probability works.

The die looks like this...
It has dots numbering 1, 2, 3, 4, 5, 6.

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What are all of the possible numbers you can get when you roll a die? Click to choose your answer.

Is any one number more likely to come up or are they all equally likely? Click to choose.

How many times will each number come up if we roll the dice 30 times? Click to make your prediction.

 

  

Probability begins with a
prediction about what
may (or may not) happen.
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How did you come up
with your prediction?

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Let’s check your prediction by playing my game. Here’s how to play Pin the Tail on the Tiger...

1.   Each person has a number that they drew from the bag. What is your number?

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2. We will roll a die to see which number gets to move one space toward the Tiger.
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3.   Click one box next to the number rolled on the die.
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4.   The person whose number comes closest to the Tiger after thirty rolls of the die,
wins the game.

 

 

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The next step in
probability is to
test your prediction
and see if it flies.

 

Click here to play
one round together.

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Let’s try it once together.

1. Here is one roll of the die. Since the roll is a two, 2 wpeD.gif (1107 bytes) gets to move
one space toward the Tiger.
       wpeC.gif (1094 bytes)

wpe16.gif (2513 bytes)

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2.   Click one box on the game next to   wpe11.gif (886 bytes)
   the number rolled on the die. Like this....                            2wpeA.gif (1107 bytes)

3.   Now you are ready to play...

Pin the Tail on the Tiger.

Make predictions...
Which number do you
predict will "win"
the game?
Click to predict
the winning number.

1

2

3

4

5

6

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Here we go!

1. Here are five rolls of the dice.
wpeC.gif (1094 bytes)wpe12.gif (1139 bytes)wpe13.gif (1116 bytes)wpe14.gif (1086 bytes)wpe15.gif (1086 bytes)

wpe6.gif (2477 bytes)

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2.   Click one box on the gameboard next to       each of the numbers rolled on the dice.

That's... 2, 6, 4, 1, 1.

3.   Look at the gameboard of...

Pin the Tail on the Tiger.

What do you see?

Which numbers were rolled the most?
Which numbers were rolled the least?
Which numbers weren't rolled at all?
These are called
true statements.

PE03534_.WMF (2486 bytes)In probability,
look at what is really happening and make
TRUE STATEMENTS
                or tell facts about the data.

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Now you are cookin'! The gameboard shows the results of the last six rolls of the dice.

1. Here are the next ten rolls of the dice.
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wpe6.gif (2477 bytes)

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2.   Click one box on the gameboard next to       each of the numbers rolled on the dice.

That's...1, 5, 5, 4, 2, 3, 4, 5, 2, 6

3.   Look at the gameboard.

What true statements can you say about the rolls of the dice so far?

Choose three true statements.


Which number is "winning?"

PE03540_.WMF (3018 bytes)In probability,
it is very important
to record exactly
what is happening,
even if your number
                 is losing.

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It looks like number 2 is winning! The gameboard shows the results of the last sixteen dice rolls.

1. Here are the next ten rolls of the dice.wpe3.gif (3035 bytes)

wpe6.gif (2477 bytes)

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2.   Click one box on the gameboard next to each of the numbers rolled on the dice.

That's...1, 3, 1, 4, 6, 3, 4, 5, 2, 6

3.   Look at the gameboard.              
What is one true statement you can say about the rolls of the dice?

PE03513_.WMF (3780 bytes)In probability,
you can change your prediction based
upon the data.
Which number will "win?"
Click to change your prediction.
1          4
2          5
3         
6


Predictions
are
not right
OR wrong.

A prediction
based on data, is
an "educated guess",
NOT a "wild guess."
What is your guess?

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Numbers 1, 2, and 4 are winning! The gameboard shows the results of the last 26 dice rolls.

1. Here are the last four rolls of the dice.
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wpe6.gif (2477 bytes)

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2.   Click one box on the gameboard next to each of the numbers rolled on the dice.

That's...4, 3, 1, 4

3.   Look at the gameboard.

Which number "won" the game?  

If we played the game again, would we get the same results?

Do you think the die
is fair or unfair?

Why?

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Now we can look at how probability works with the data on the "Pin the Tail on the Tiger" Graph.

Here are the results of the game on this graph.     wpeE.gif (913 bytes)PE03509_1.WMF (7434 bytes)In probability,
you must organize the data
to see patterns.
Let's create a table to organize the data.

Tail Number Number of wins for each number on the die or Tiger Tail Number Total number of dice rolls
1

 

30
2

 

30
3

 

30
4

 

30
5

 

30
6

 

30

Pin the Tail on the Tiger Graph

wpe6.gif (2477 bytes)
wpe3.gif (904 bytes) wpeD.gif (904 bytes) wpeE.gif (904 bytes) wpeF.gif (904 bytes) wpe10.gif (904 bytes)
wpe11.gif (904 bytes) wpe12.gif (904 bytes) wpe13.gif (904 bytes) wpe14.gif (904 bytes) wpe15.gif (904 bytes)
wpe18.gif (904 bytes) wpe19.gif (904 bytes) wpe1A.gif (904 bytes) wpe1B.gif (904 bytes)
wpe1C.gif (904 bytes) wpe1D.gif (904 bytes) wpe1E.gif (904 bytes) wpe1F.gif (904 bytes) wpe20.gif (904 bytes) wpe21.gif (904 bytes) wpe22.gif (904 bytes)
wpe23.gif (904 bytes) wpe24.gif (904 bytes) wpe25.gif (904 bytes) wpe26.gif (904 bytes)
wpe27.gif (904 bytes) wpe28.gif (904 bytes) wpe29.gif (904 bytes) wpe2A.gif (904 bytes)
wpe9.gif (3306 bytes)

                               1      2      3      4        5      6      7

Wins for 30 Dice Rolls Previous Page |  Next Page

 
 
 
 
 
 
 
 
 
 
 
 

 

 

 

 


 

Now let's put that data into numbers like mathematicians do.
One way to see how those numbers work is to create a pie chart with the data, like this...

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What does the data on the pie chart show us?

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The pie chart shows a
whole pie cut into parts.

The whole pie stands for the total number of dice rolls.
What was the total number of dice rolls?

Thirty dice rolls equals the whole or one on the pie chart.

BS01177_.WMF (3272 bytes)The pieces of the pie chart show the parts of the whole or the number of wins for each number rolled on the die out of 30 times.

How do the pieces of the pie chart look to you?

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Mathematicians call numbers that show the pieces of the whole...
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FRACTIONS.  Let's look at the
Number Line of Probability again to see how FRACTIONS work in probability.

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LET'S FIND THE FACTS:
What is the probability of rolling a zero on a standard die?
What is the probability of rolling a 1, 2, 3, 4, 5, or 6 on a die?

The QUESTION is...
What is the probability of rolling
just one of the numbers on the die?
Numbers greater than zero but less than one can be called FRACTIONS.


PE03535_.WMF (5022 bytes)When probability
is written as a fraction,
it means that the likelihood
is less than one
or not a sure thing.
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Let's look at this pie chart. It shows the results from our game.
Each number on the die is shown next to the probability of rolling it.

wpeD.gif (4424 bytes)

The probability is shown as a FRACTION like 1/6.
The probability is read like this...
There was a 1 out of 6 probability of rolling a 1 or 2.

 

The pie chart shows the probability of rolling
a 1or 2 was...
                           1/6
OR 1 out of 6.

What was the probability of rolling a 3, 5, or 6?

What was the probability of rolling a 4?

PE03542_.WMF (3912 bytes)Probability can be
shown as fractions,
percentages, or ratios.

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Mathematicians predict the probability of rolling any one number on a die as...

1 / 6 or 1 out of 6 probability
   of rolling any one number on the die. 

Here is what it means...

1
When you roll a die, you can only roll one number on the die.
/
out of
6
The total number of  possibilities on the die.


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Did our experiment almost match the probability predicted by mathematicians?

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BS00825A.GIF (3117 bytes)The results of our game did not exactly match the probability that mathematicians predicted we would get when rolling a die.
What does this mean?
Did we do something wrong?

Explain what you think happened in your own words.

PE03504_.WMF (5800 bytes)In probability,
the work is never done.
Keep fishing for the answers.
The best way to check out how probability works is to play the game again and again and again.
Let me know what happens!

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