Warning: Do not read other posters' comments unless you give up since it usually contains the answer. Clutchcity.net posters are very smart. This is a simple riddle, yet it brings so many debates. The answer seems to be against logic. I am the quiz master, and you are the quiz participant. Here is the rule of the quiz: There are three doors, and one of the doors has a BMW prize. If you can correctly predict which door has the car, you'll win the prize. After you pick one door randomly, I don't let you open the door to see what's inside yet. What I do is I open one of the two remaining doors that you don't choose, and I know for sure that the door I open is empty (i.e. no car prize inside). Therefore, after I open one empty door of the two remaining doors, you'll be left with two closed doors. Now, I propose you an offer: 1. Do you still want to open the door you originally choose 2. Or do you want to switch to the other door. 3. Or you don't care because you think the probability of the two closed doors having the car prize inside is the same (50-50). When possible, explain why you choose one over the other. Some Notes: * I as a quiz master knows exactly which door contains the car prize. Therefore when I open one of the two remaining doors, I know for sure the car prize is not there. * This rule (e.g. I propose you an offer) always applies in every game. So don't think that I am trying to confuse you with the offer since you choose the correct door with the car prize inside. Even if we repeat this quiz 10 times, I will always open one empty door and make you a proposal.
We already did this one here a few weeks back, and whoever tells you the right answer (always switch because odds are 2 to 3 you'll end up with the right door), Major should get credit for the best layman terms explanation.
I would say the odds are 50/50. But since this is a riddle, I'll try something different. I'm going with Pole's logic. Before you tell us anything, there is a 33% chance that the door we picked has the BMW and a 67% chance that the other 2 doors has the BMW behind it. Since you already know you are going to unveil a door that DOESN'T have a BMW behind it, the odds stay the same when we are down to 2 choices. Our original choice has a 33% chance while the other door a 67% chance. So it is better to switch and pick the other door.
no need for the pardon; you're doing a great job. I was just letting you know.....and throwing some more well deserved credit Major's way.
Yes, you are correct. This is the same as if I propose you if you want to switch the one door you choose to the other two doors you don't choose. The difference between the question and this is of course instead of opening the two doors yourselves, I open one door for you.
Pole -- thanks! Although I have to say, I'm very glad you posed that question a couple of weeks back. Until then, I always insisted the other answer because I had never actually tried to figure out the math behind it!
You want to switch doors. The first door you choose has a 33.3bar% chance of being the correct door. The other door has a 66.6bar% chance of being correct.
To make this much more obvious that you should switch the door: Assume there are 100 doors. You choose one door randomly. The probability there is a car inside is only 1/100. The rest of the doors you don't choose together have 99/100 probability of a car being inside one of those. Since I am the quiz master and I know exactly where the car is, I'm doing you a favor by opening the other 98 doors you don't choose that I know for sure have no car inside. Now you end up with two closed doors. The one closed door you originally choose (1/100 probability), and the other closed door that I do not open. If you think it's a 50-50 chance of a car being inside one of those two doors, you're wrong. The other closed door you don't choose has 99/100 probability of having a car inside. Like I said, this is the same as if I am offering you to trade one door you choose (1/100 prob) with all other 99 doors you don't choose (99/100). If I were to make that offer, you'll definitely be willing to make the trade. What's so different now with me opening the 98 out of 99 doors that you don't originally choose for you.
