This is really late, but is a problem that’s always interesting & fun to do with kids (or adults 🙂 ) Question #2 has me working though…
In the interest of “fairness” Egan allows who does the dishes to be a matter of chance. The set up is quite simple: In a bag containing two blue marbles and three white marbles, two marbles are drawn. If the two marbles are the same, Egan does the dishes, and if the two marbles are different, another member of the Chernoff household does the dishes. Now, if you have ever noticed how soft and smooth Egan’s hands are, this is not because they are soaking in PalmoliveTM all the time! In fact, just recently, other members of the Chernoff household are wondering if the game they play every night is fair…is it? Here’s the weird part, Egan has a perpetual disclaimer: “If you have issues with the game, we can always change the number of marbles in the bag.” Before you pass judgment on Egan, determine if the game is fair. If the game is not fair, and you want to help out the other members of the Chernoff household, make the game fair.
• Question #2:
There are x blue and y white marbles in a hat. Two marbles are drawn at once. For what values of x and y will the game be unfair? For what values of x and y will the game be unfair? You may provide several examples before you generalize. What values of x and y have one person doing the dishes three time more than the other?