Okay, for the good of your education I must share with you one of the most entertaining ood logic puzzles: The Monty Hall Problem.
You've landed a spot as a contestant on Let's Make a Deal (you had mace in your purse and won $100!). You're given three doors and behind one of them is a brand new car (a 1980 Chevrolet Impala! The car that won the cold war!). Mr. Hall gently places his weathered hand on your shoulder and asks you to choose a door. You pick door number three because the number three reminds you of how many moments you've been truly happy in your life. Monty then reveals door number one to reveal a goat (sexy)! You've seen the show, so you know he always reveals a losing door first. Monty places his arm around your shoulders and squeezes ever so subtley. "Well miss," he says, "do you want to stick with the door you've chosen or do you want to switch?"
You're faced with a dilemma. Should you switch or not? You really want that Impala. It'd sure make hauling your family to the local Western Sizzlin easier. Your VW Rabbit just isn't cutting it. Naturally you want to choose whatever gives you better odds at winning that brand new car. What to do then?
Does switching lower or improve your chances?
Does it matter?
The answer? You're better off switching. By switching you have a 2/3 chance of winning, whereas by sticking with the door you originally chose, you have a 1/3 chance of winning. I'll let you figure it out on your own, but the key lies in the fact that Monty knows where the car is and always reveals the losing door that you haven't chosen. Also, imagine that instead of 3 doors to start with there are 100 and monty reveals 98 of them. Which way do your intuitions drive you in that scenario?
After doing what's more likely to get you that car, Monty reveals the door your chose: a brand new goat! Sorry, we can't all have happy endings. At least your husband is finally going to rehab!

