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.

Probability is everywhere, but my game, Pin the Tail on the Tiger

can help us see how probability works. Okay,
who goes first?

If we put these numbers in a bag... 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... 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? yes no What number did you pick? 1 2 3 4 5 6

 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. 1, 2, 3, 4, 5, 6 0, 1, 2, 3, 4, 5 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Is any one number more likely to come up or are they all equally likely? Click to choose. Some numbers are more likely. All numbers are equally likely. 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. 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. 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.   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.       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? 1 and 2 were rolled the most. Number 1 was rolled the most. Number 2 was rolled the most. 4 and 6 were rolled the most. 3 and 5 were rolled the most. Which numbers were rolled the least? 1 and 2 were rolled the least. 4 and 6 were rolled the least 3 and 5 were rolled the least. Which numbers weren't rolled at all? 1 and 2 were not rolled at all. 4 and 6 were not rolled at all. 3 and 5 were not rolled at all These are called true statements. 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.   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. Two was rolled four times. Two was rolled more than the others. Two is a lucky number. 1, 4, and 5 were rolled 3 times. 1, 4, and 5 were rolled equal times. Number 2 cheated. 3 was only rolled once. 3 is an unlucky number 3 was rolled the fewest times. Which number is "winning?" 1 2 3 4 5 6 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.   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? educated guess wild 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.   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.  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

 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... What does the data on the pie chart show us? 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? 3 4 5 6 7 30 Thirty dice rolls equals the whole or one on the pie chart. 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? about equal in size exactly equal in size totally unequal in size

 Mathematicians call numbers that show the pieces of the whole... FRACTIONS.  Let's look at the Number Line of Probability again to see how FRACTIONS work in probability. LET'S FIND THE FACTS: What is the probability of rolling a zero on a standard die? 0 1 What is the probability of rolling a 1, 2, 3, 4, 5, or 6 on a die? 0 1
 The QUESTION is... What is the probability of rolling just one of the numbers on the die? The probability is 0. The probability is 1. The probability is a number between 0 and 1. Numbers greater than zero but less than one can be called FRACTIONS. When probability
is written as a fraction,
it means that the likelihood
is less than one
or not a sure thing. | 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. 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? 1/6 OR 1 out of 6 1/7 OR 1 out of 7 1/4 OR 1 out of 4 What was the probability of rolling a 4? 1/6 OR 1 out of 6 1/7 OR 1 out of 7 1/4 OR 1 out of 4 Probability can be
shown as fractions,
percentages, or ratios.

 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. Did our experiment almost match the probability predicted by mathematicians? yes no 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. 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!