Pin the Tail on the Tiger

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?"

I will help you learn all about probability.
What do *you* think probability is?

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...
	There is a 20% chance of rain today.
	The ratio of a nickel to a dime is 2 : 1.
	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?

Probability looks at
the chances of an event
happening or not happening.
"Will I hit the ball or not?"

Probability is everywhere, but my game,

Pin the Tail
on the Tiger

can help us see how probability works.

BS00825A.gif (3117 bytes)
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? |

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

wpeC.gif (2400 bytes)

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?
	Did you pick your number for the game? What number did you pick?

Now we are ready to play the game.	How do we play?
Well, it’s like "Pin the Tail on the Donkey."
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.

Probability looks at
all of the possibilities.

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.
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?

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?

2. We will roll a die to see which number gets to move one space toward the Tiger.

3. Click one box next to the number rolled on the die.
1

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.

Let’s try it once together.

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

2. Click one box on the game next to
the number rolled on the die. Like this.... 2

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

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)

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.

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In probability,
look at what is really happening and make
TRUE STATEMENTS
or tell facts about the data.

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.
wpe17.gif (2848 bytes)

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?"

In probability,
it is very important
to record exactly
what is happening,
even if your number
is losing.

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)

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?

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?

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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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?

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. 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

1 2 3 4 5 6 7

Wins for 30 Dice Rolls |

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.