Problem of the Week-1: The Money or the Goat?

This classic puzzle from probability theory is known as the Monthy 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 3 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?

Give a careful reasoning to justify your answer.

Posted: 1/20/04

Submit your answers (by e-mail or hard copy) before 4 pm on 1/30/04 to Noah Aydin.

Mathematics Dept.