Hey! Do you remember when we played that game,
Pin the Tail on the Tiger
at the birthday party?

                                              Yeah, that was fun and I learned
                                       more about probability.

Me too! But now I'm confused.

              You're lyin'!

AN03517_.WMF (12818 bytes)No, I'm not, I'm Tiger. Can you help me answer a few questions I have about probability?


AG00198_.GIF (6343 bytes)
Sure, I can help you with
probability,
that's my favorite subject!

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AN03518_.WMF (10166 bytes)Well, I played the game again and I didn't get the same results.
The number 2 die won my game.

The number 3 die won my game.

Did anyone out there get different results?
Which number won your game?

                                                        Of course, probably everyone
                                      got different results.

Why does that happen?

 
 
Why do you think each time the game is played, there are different results?
EN00892_.WMF (3670 bytes)
 

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EN00191_.WMF (5356 bytes)I think it has to do with likelihood. Am I right?
                                                              I think my funny dice can help you with this.                                                               See what you think...

I have three funny dice. Here is what each die has on its six sides.

How many chances do you have to roll a 1 on this die?

wpe10.gif (1983 bytes)

1
side has one dot

out of 6
sides in all
How many chances do you have to roll a 1 on this die? wpeE.gif (2027 bytes)
sides have
one dot
out of
sides in all
How many chances do you have to roll a 1 on this die? wpe11.gif (2056 bytes)
sides have
one dot
out of
sides in all

Okay, I count the
number of sides
that have
the possibility I want

out of

the total number of possibilities.

AN03535_.WMF (12118 bytes) Is that right?

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You are thinking! Now let's look at a standard die.
wpe3.gif (2214 bytes)
AN00023_.WMF (11140 bytes)Remember you are looking for the number of chances you have of

rolling one result
out of
all of the possible results.

BS00863A.GIF (867 bytes)

The number of
a possibility

out of

all the possibilities

wpe18.gif (938 bytes)

1 chance out of 6 possibilities
wpe19.gif (937 bytes) chance out of  
wpe1A.gif (940 bytes) chance out of  
wpe1B.gif (943 bytes) chance out of  
wpe1C.gif (944 bytes) chance out of  
wpe1D.gif (945 bytes) chance out of  

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So, that is why mathematicians say the probability of rolling any one number on a die is a

wpeD.gif (973 bytes)
or
1 out of 6 probability
 

Here is what that means...

wpe1F.gif (1131 bytes)    When you roll a die, there is  wpe1B.gif (860 bytes)one chance of rolling any
        one result
wpe1C.gif (860 bytes)out of
wpe1D.gif (860 bytes)the total six possibilities


wpe2A.gif (4596 bytes)wpe19.gif (2094 bytes)

wpeD.gif (973 bytes)
probability is shown for each number on this circle graph. What do you notice about the size of each piece?
If each number on the die has a 1 out of 6 probability,
what is the likelihood of rolling any one number compared to another?  Previous Page |  Next Page

 



 

 

 

 

 

Here is how a circle graph works to show probability...

 BS00876A.GIF (1720 bytes)
The circle graph shows a
whole circle cut into parts.

The whole circle stands for...
the total Probability of WINS
when you roll a die.

To count the total number of possibilities when rolling a die, count the number of pieces on the circle graph.

AN03559_1.WMF (4792 bytes)Oh, now I get it! The total number of possibilities equals the  whole circle graph.

wpe27.gif (4596 bytes) wpe19.gif (2094 bytes)

Use the circle graph to find the possibilities when rolling a die.
What are the total number of possibilities?
 
        
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                       Good for you! The pieces of
                     the circle graph show even
                   more about probability...

BS01177_.WMF (3272 bytes)The pieces of the circle graph show the parts of the whole or each different possibility when rolling a die.

How do you find the probability of a number on the circle graph?

Here's how...

1. Look at the circle graph KEY.
2. Find the  wpe3.gif (1003 bytes)next to the color wpeD.gif (862 bytes).
3. Find the color  wpe18.gif (862 bytes) on the circle graph.
4. The number next to the color says...
wpe2D.gif (934 bytes)or 1 out of 6 probability of rolling a wpe19.gif (1003 bytes).

wpe25.gif (4596 bytes) wpe19.gif (2094 bytes)

What is the probability of rolling a wpe1A.gif (937 bytes)?

What is the probability of rolling a wpe1B.gif (940 bytes)?
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If there is a 1 out of 6 probability of rolling any number on a die, then how did the wpe1C.gif (943 bytes)"win" our game?

        That's a good question!

If the real probability of rolling any number on a die is 1 out of 6 probability, all of the numbers should win. Shouldn't they?

                       AN00800_1.WMF (13736 bytes)      You are really thinking now. Let's look at the results of our game on this circle graph.

wpe1D.gif (4957 bytes) wpe1E.gif (2989 bytes)

Click in the boxes to select the sets of numbers that were equally likely in our game.
          

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If probability was exact, the likelihood of rolling any number in our game would be equally likely, but that didn't happen.

                                   Let's look at this circle graph.  It shows the results     for rolling each number in our game.

wpe2E.gif (5346 bytes)wpe29.gif (2989 bytes)

The circle graph shows that the probability of rolling a wpe26.gif (938 bytes)was a
wpe31.gif (967 bytes) or 5 out of 30
probability.

What was the probability of rolling a 2?

What was the probability of rolling a 3?

What was the probability of rolling a 4?

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                                   You are getting it. Keep going!

wpe2F.gif (5346 bytes)wpe29.gif (2989 bytes)
Look at the circle graph and key and then click to answer these questions.
What was the probability of rolling a 5?
What was the probability of rolling a 6?
EN00932_.WMF (14366 bytes)This probability stuff is really starting to jingle.

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Here is the circle graph that shows the results from our game where we rolled the die 30 times. Here is the circle graph that shows what mathematicians say is likely to happen or the probability of rolling any one number.
wpe30.gif (5346 bytes) wpe2B.gif (4711 bytes)
Did our experiment exactly match the probability predicted by mathematicians?

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The results of our game did not exactly match the probability of the mathematicians. What does this mean? Did we do something wrong?

Explain what you think happened in your own words.

 
SO00247_.WMF (23464 bytes)           Remember, probability is not                exact.   The more games you play,                the closer the die rolls would come                 to the mathematician's                
            probability
.                                   

Okay, so let's play the game 300 more times.

You're lyin'.

No, I'm not, I'm Tiger! AN03520_1.WMF (11700 bytes)
We don't have to play right now.
We can play later.
Besides, it's time for my catnap.

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