So, you’ve got common sense. Uh huh.
Well, we’ve established that you have common sense, because you are after all reading this blog. So, I’ve got an offer that I know you will nail first shot!
Here’s the situation and the rules:
- There are three doors in front of you and you do not know what is behind each.
- Two of the doors have a goat behind them.
- One of the doors has a nice sports car.
- You start by selecting one of the doors.
- I then open one of the other two doors to show you a goat.
- You are then given this choice: would you rather stay with the door you originally picked – or would you rather switch to the other unknown door?
Now, if your common sense is like mine, your response is that it makes no difference whether I stay or switch, because I picked randomly so I have even odds of picking a car or a goat regardless of whether I stay with my original door – or whether I switch to the other available door.
I’m here to tell you that you double your odds if you switch!
Now, what kind of snake oil is this that I’m trying to sell you? Well, let’s lay out the cases first:
| Initial Pick | Stay | Switch |
| 1 | Goat | Car |
| 2 | Car | Goat |
| 3 | Goat | Car |
Well, how about that! If I switch, I have two chances out of three of getting a Car. If I stay, I have one chance out of three of getting a Car.
Think about it. Counter intuitive until you ponder for awhile. How many other situations do we face that are like this? What does this imply about our decision making, our common sense – and our prejudices?
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Tags: Choices, Prejudices, Probabilities
But I want a goat!
No pollution and a new blanket or overcoat grown while he cuts the grass…. and I forgot, free fertilizer!
Grannymar´s last blog ..Shapely Legs
I don’t want any old goat! Pick me a good one.
Grannymar´s last blog ..Shapely Legs
Grannymar, for you I’ll find the Cadillac of goats! You know, from back when Cadillac was good…
We have native grass & never mow so I don’t want a goat. We have a 2 car garage, have 2 cars & there are 2 of us here, so I don’t want a car.
My husband likes game shows because he knows the answers. I don’t.
Tom has explained the 2/3 chance if I switch, many ways, but I will NEVER understand it. I have intuition about other things. Intuition doesn’t solve that problem, logic does. I always thought I was logical.
I know that prejudices take common sense “to hell in a hand basket” to quote Carol.
If I recognize that it’s not logical (a whim) then I have common sense???
bhb, first, bravo for the way you wrapped your arms around this question. Second, I would never attack your common sense. What I’m pointing out is a problem that all of us as humans have that leads us to inconsistency and sometimes to bad decisions or bad judgments. I think it is enough to have the humility to be aware that “common sense” pronouncements aren’t always “the truth” and that we are all struggling together to make sense of a pretty complex world. What one person nails right on the nose, the other does not. And, in the next situation, the roles are often reversed.
It’s just part of the dance of understanding!
Grannymar, one more thought. If you want a goat – increase your odds by not switching doors. But don’t ask me to cheat for you and go find a goat for you and just give it to you! I have my integrity!
But, for the right price…
Your father will be the first to tell you that I have never had anything to do with logic and just say the first thing that comes to my withered brain. I want a goat…..sure would save me a lot of money every summer. But, maybe not. I’d have to have a herd of goats to cover this yard and I don’t like to milk them so they would all have to be billy goats and they would probably get out of the fence and attack the neighbors and we would be sued……….to heck with the whole thing. lol
Corky
Short and simple. I would switch from my first choice. Why? The odds actually improve by your showing me the door with the goat. Now I have 2/3 chance of winning rather than the original 1/3!
The advantage of being an Indian of my generation is that your thinking gets to be logical with all the mathematics that you were taught when youwere in school. It became more or less mechanical for most of us. For instance, except for very long calculations, I do not use a calculator as the tables up to 20 X 20 that I was forced to learn and also to do mental arithmetic for fear of severe punishment, enables me to work out sums faster than taking out a caluculator, pressing the buttons and reading out the result. I actually feel sorry for sales assistants who cannot do this!
That is the logical part of the answer! The fun part of the answer, I do not want either the goat or the car. I have no place for either in my life. There BHB, another like you!
rummuser´s last blog ..Management And The Wife.
Incidentally, commonsense is the most uncommon of commodities available now a days! The world would not be in the mess it is had it not been so.
rummuser´s last blog ..Management And The Wife.
The variaton actually assists in the increase of probabilities in our favour. The logical mind would tell you that, but then again math doesn’t take into account the uncommon circumstances of stress that presents itself to a person in such a situation, the fear of failure that plagues him and so many other such factors. The point is simply this, we are humans and not robots
Common sense is uncommon as Ramana sir has pointed. From my point of view, I go by it with not one but many principles. “Do onto others as you would want others to do onto you” may perhaps be a good example of common sense. But I have never given the term that much thought actually.
Ashok´s last blog ..The day that wasn’t
Ashok, give me a robot any day for these kind of challenges. Just imagine driving away in a car!
rummuser´s last blog ..A Soldier Comes Home.
@Ramana sir: I suppose if there is a pretty lady who acts as the model in opening the doors in this game show, you would invite her on the drive as well?
kidding
Ashok´s last blog ..The day that wasn’t
Why the ‘kidding’ qualification? But of course I will.
rummuser´s last blog ..THANK STEREOTYPING IT’S FRIDAY!
Conrad, I just finished a book that explains the logic behind the conundrum you posed, as well as it’s history. It first showed up in Ask Marilyn! I think you’d be very interested in this book, _The Drunkard’s Walk: How Randomness Rules our Lives_ by Leonard Mlodinow. He exposes many fallacies in the way we interpret data in our lives, as well as takes us on a tour of the development of theories of probability and statistics. Very readable and quite fascinating.