Ice Cream Prices
This is a GeoGebra adaptation of Allan Rossman's presentation at Simulating at Serenbe III
Table of Contents
- Ice Cream Prices
- Ice Cream Prices (Intuition)
- Ice Cream Prices (Simulation)
- Ice Cream Prices (Mathematics)
- Free Ice Cream
- Free Ice Cream (Intuition)
- Free Ice Cream (Simulation)
- Free Ice Cream (Mathematics)
- Average Price
- Average Price (Intuition)
- Average Price (Simulation)
- Average Price (Mathematics)
- Three Dice
- Three Dice (Intuition)
- Three Dice (Simulation)
- Three Dice (Mathematics)
- More Dice
- More Dice (Intuition)
- More Dice (Simulation)
Ice Cream Prices (Intuition)
Suppose that you have only 50 cents in your pocket and you want to buy an ice cream cone. The owner of the ice cream shop offers a random price determined as follows: You roll a pair of fair, six-sided dice, and the price is the larger number followed by the smaller number (in cents). We will approximate, and then determine, the probability that you’ll be able to afford the ice cream cone.
Explain what the word “probability” means in this context.
Make a guess for the probability that you will be able to afford the ice cream cone.
Describe how you could approximate this probability with a pair of fair, six-sided dice.
Free Ice Cream (Intuition)
Now suppose that I offer to pay for your ice cream cone if the price is an odd number. Recall, the owner of the ice cream shop offers a random price determined as follows: You roll a pair of fair, six-sided dice, and the price is the larger number followed by the smaller number (in cents).[br]
Do you think it’s more likely that I will pay for your ice cream cone, or that I will not pay for your ice cream cone?
Make a [b]guess[/b] for the probability that I will pay for your ice cream cone. This is a "what-does-your-gut-tell-you?" type of guess.
Average Price (Intuition)
Recalling how the owner of the ice cream shop offers a random price determined as follows: You roll a pair of fair, six-sided dice, and the price is the larger number followed by the smaller number (in cents). [br][br][color=#333333]Now let’s consider the average price of an ice cream cone, using this random process.[/color]
Make a [b]guess[/b] for the average price that would result from repeating this random process a very large number of times. Again, this is a "what-does-your-gut-tell-you?" kind of guess.
Describe how you could use simulation to approximate this average price.
Three Dice (Intuition)
Now suppose that the owner of a new, competing ice cream shop determines a random price by rolling three fair, six-sided dice. Your price (in cents) will be the largest number followed by the smallest number.
Would you expect prices to generally be higher at the new shop or the old shop? Explain why.
How would you expect the probability that you can afford an ice cream cone to change? Explain your reasoning.
How would you expect the probability that I pay for your ice cream cone to change? Explain your reasoning.
How would you expect the average price of an ice cream cone to change? Explain your reasoning.[br]
How would you expect the variability (as measured by standard deviation) in ice cream cone prices to change? Explain your reasoning.
More Dice (Intuition)
Now think about letting the number of dice get larger and larger, still with the rule that the price is the largest number followed by the smallest number.
What do you expect to happen to the probability that you can afford an ice cream cone as a function of the number of dice? Explain your reasoning.
What do you expect to happen to the probability that I pay for your ice cream cone as a function of the number of dice? Explain your reasoning.
What do you expect to happen to the average price as a function of the number of dice? Explain your reasoning.[br]
What do you expect to happen to standard deviation of prices as a function of the number of dice? Explain your reasoning.
What do you expect to happen to the probability distribution of the price as the number of dice gets quite large? Explain your reasoning.