October 21, 2014
Problem of the Week
October 21, 2014
Your eccentric uncle Pascal wants to celebrate your birthday with a special present. He lays on the table 2 top hats, 2 one dollar bills, and 2 one-hundred dollar bills. You are asked to place all the bills in the top hats in any way you choose. Your uncle then tells you to close your eyes as he shuffles the 2 identical top hats and the bills inside. You then select your birthday present in the following way. You pick a top hat at random and then select a bill from the inside of the top hat with your eyes closed. How should you arrange the bills so as to maximize the average value of your birthday present? What is this average value?