The following problem appeared in the news column “Ask Marilyn” on September 19, 2010. Four identical sealed envelopes are on a table. One of them contains a $100 bill. 

You select an envelope at random and hold it in your hand without opening it. Two of the three remaining envelopes are then removed and set aside, unopened. You are told that they are empty. You are given the choice of keeping the envelope you chose or exchanging it for the one on the table. 

What should you do? a) Keep your envelope. b) Switch it. c) It doesn’t matter.
Write a simulation to find the probability of selecting the $100 bill when you switch. Confirm the results of your simulation with an exact analysis.