Lesson of The Week: Choices

Have you ever watched "Let's Make a Deal". It's a game show where you can take the prize that is shown to you or go for a mystery prize behind a door. Well consider this scenario. You have three doors in front of you. One door has gold behind it and the other two have coal behind them. You initially choose the middle door. Now before you can open the door, the right door opens, showing a bunch of coal. Now you're allowed to pick the other door instead. Should you?

You might think that it's all the same chance of having the gold, but statistically speaking, that isn't right. You actually have a better chance when you choose the other door the second time instead of staying with your first pick. Why? Well, initially, you are deciding between 3 doors, meaning you have 33% chance of getting the right door. That's not good, but you gotta be in it to win it!

Once one door is opened, you now have a 66% chance of choosing the right door. If you stay with the door you had, then you're stuck with your original 33% guess. If you choose the other door, then because you already know that the open door is wrong, you really have two doors in you possession, the one you selected on the second guess and the one that was opened. There really is only one door you don't control, and that's your original guess. Therefore you chance improves to 2 out of 3 or 66%.