Riddles: Monty Hall and Two Boys

For more than two decades, the Monty Hall problem stood as my favorite probability riddle.  But recently, the Two Boys riddle has replaced Monty Hall as my favorite.  Both are excellent riddles that exploit the same underlying weakness in the listener—a willingness to (incorrectly) dismiss information as irrelevant.

In this post, I’ll present each of the two riddles.  Tomorrow, I’ll post the solutions.

Let me know whether or not you think you’ve found the answers and how long it took you to find them.

Monty Hall Problem

For those of you who might not remember, Monty Hall was the host of the television game show, Let’s Make a Deal.  In this show, the contestant that did the best during the show was offered a chance to win a “grand prize” such as a car, or a boat, or a big vacation package.

In a frequently used scenario, Monty would present the top contestant with a stage containing three doors: door #1, door #2, and door #3.  Monty would describe the fabulous grand prize that lies behind one of the three doors.  He would also describe two “dud” prizes, perhaps a goat, or a pair of used tennis shoes, that lie behind the other two doors.  The contestant was offered the opportunity to choose any door and have whatever prize was found behind that door.

Inevitably, after choosing a door, Monty would provide one more twist.  He would tell the contestant, “Before I show you what is behind the door you’ve chosen, let me show you what is behind one of the other doors.”  At this point, Monty would open a door to reveal one of the dud prizes, and say, “Now, before we see what’s behind your door, would you like to change doors or stick with your original choice?”

Here begins the riddle:  What should the contestant do?  And if the contestant follows you’re advice, what are the odds of winning the grand prize?

Two Boys Riddle

This riddle is very straightforward:  You meet a man and begin to talk about your respective families.  He informs you, “I have two children, one of which is a boy born on a Tuesday.”  What are the odds that the man has two boys?

This is my current favorite probability riddle because initially, I was quite convinced that I understood the riddle completely and knew the correct solution.  But I was wrong.

Do you have another favorite probability riddle?  Please share it in the comments.