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.

How would you expect the variability (as measured by standard deviation) in ice cream cone prices to change? Explain your reasoning.