Lions, Tigers, and Probability

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'!

No, I'm not, I'm Tiger. Can you help me answer a few questions I have about probability?

Sure, I can help you with
probability,
that's my favorite subject!

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?

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?	1 side has one dot	out of	6 sides in all
How many chances do you have to roll a 1 on this die?	sides have one dot	out of	sides in all
How many chances do you have to roll a 1 on this die?	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.
	Is that right?

You are thinking! Now let's look at a standard die.

Remember you are looking for the number of chances you have of

rolling one result
out of
all of the possible results.

The number of a possibility	out of	all the possibilities
1 chance	out of	6 possibilities
chance	out of
chance	out of
chance	out of
chance	out of
chance	out of

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

or
1 out of 6 probability

Here is what that means...

When you roll a die, there is one chance of rolling any
one result
out of
the total six possibilities.

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? |

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.

Oh, now I get it! The total number of possibilities equals the whole circle graph.


Use the circle graph to find the possibilities when rolling a die. What are the total number of possibilities? \|

                       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 next to the color .
3. Find the color on the circle graph.
4. The number next to the color says...
or 1 out of 6 probability of rolling a .


What is the probability of rolling a ?
What is the probability of rolling a ? \|

If there is a 1 out of 6 probability of rolling any number on a die, then how did the "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.


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

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 was a
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?

You are getting it. Keep going!

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?

This probability stuff is really starting to jingle.

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.

Did our experiment exactly match the probability predicted by mathematicians?

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!
We don't have to play right now.
We can play later.
Besides, it's time for my catnap.