Exploring Probability Through Dice Rolls
Welcome!
In this activity, you will explore how the probability of sums changes as you roll different numbers of dice. Use the applet below to:[list][*]Change the total number of dice being rolled.[/*][*]Observe how the distribution of sums changes as you roll different numbers of dice.[/*][*]Record your data and analyze the results by updating the provided t-chart and histogram.[/*][/list]
Dice Roll Applet
[list=1][*][b]Drag the dice[/b] onto the screen to select how many you want to roll. (Required 1,2,and 3 dice)[/*][*][b]Click the roll icon[/b] to roll all the selected dice at once.[/*][*][b]Record the sum[/b] of the dice on your T-chart.[/*][*][b]Repeat Steps 2 and 3[/b] until you have a total of 15 entries.[/*][*]If needed, [b]use the erase tool[/b] to correct any mistakes.[/*][/list]
Now that you have recorded the sums in your T-chart, [b]plot the results[/b] for 1, 2, and 3 dice rolls on a histogram. Make sure to place each sum in the correct bar, showing how often each sum occurs for each number of dice.
What happens to the range of possible sums as the number of dice increases?
How does the shape of the histogram change as you increase the number of dice?[br][*][/*]
What do you notice about the most likely sum when rolling 2 dice, 3 dice, or more?[br]
Real World Application
Design a game where rolling x amount of dice and achieving a sum of y results in a win. Use the applet and notepad to explore how often players would win.[br]*Note: x and y will be determined by the student to create their own game.*
How likely are players to win based on your rules? What amount of dice would make the game the hardest to win?
Reflection
What surprised you most about how the number of dice affects the distribution of sums?
[*]If you had unlimited dice, what might the distribution look like?[/*]
Teacher Resources
