Cartesian Product Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

This discussion helps familiarize you with the idea of Cartesian products, by looking at how they can describe outcomes in dice, card, etc. games. Although we won’t do it here, these ideas can reappear in discussions of probability.

Suppose you flip 2 coins, say a nickel and a dime. Discuss how you could describe possible outcomes as ordered pairs. Based on those ideas, could you describe the set of all possible outcomes as a Cartesian product? If so, of what sets?

Can you extend the ideas about coin flips to rolls of a pair of dice, say a red die and a blue one? What about rolling the red die and flipping the dime?

How about playing cards — are they ordered pairs? If so, from the Cartesian product of what sets? Do jokers matter to your answer?

Finally, what if you have 3 (or more) coins or dice? (Are there decks of cards where it takes more than 2 distinct values to identify each card? If so, you can include them in this part of the discussion.) Discuss whether or how your ideas about outcomes as Cartesian products extend to those situations.