The Money or the Goat?

This classic puzzle from probability theory is known as the Monty Hall problem after the host of “Let's Make a Deal!” It was played as part of that TV game show.

Imagine you are a game show contestant with three closed doors before you. You are told that behind one of these doors is a prize of one million dollars in cash. Behind each of the other two are goats. You select a door, but before you open it, the host opens one of the two remaining doors to reveal—a goat! He now gives you the opportunity to stay with your original choice or switch to the remaining unopened door. What should you do? Switch doors or stay with your initial choice? Does it make any difference?

Double or … Double!!

A friend places before you two paper bags, both containing Tootsie Rollsd®. He tells you that one contains twice as many as the other and that you may keep the contents of one of the bags. You select a bag, open it up, and count the number of Tootsie Rolls® it contains. Your friend then gives you the option to change your mind and take instead (without peeking inside!) the contents of the other bag. Assuming you would like as many Tootsie Rolls® as possible (and you don't feel it is an insult to his generosity to switch), is it to your advantage to switch bags? Or is it better to stay with your first choice?