PROBABILITY: MONTY HALL

¿Probability? You must be a mathematician to understand it!

No!.  Probability is everywhere.  When you are searching for a parking space you take the streets with more cars parked because probability to run into a car leaving is bigger than in narrow streets.  If you get a poker you bet big because the probability to get better cards is really small.  If you have a pain you are operated because probability to die during the operation is almost zero.

As you see probability is everywhere!

Ok, ok, I agree.  So… Who is Monty Hall?

I’m pretty sure you are thinking he must be a bored and arrogant mathematician from the last century but……… no!!!!  He is a popular TV presenter who run the Tv program: “Let’s Make a Deal”. 

I’m sorry I’m confused. 

Don’t worry, Monty Hall problem is the name of a mathematical problem based on the TV program.  During the show the contestant had to choose among three doors, behind one door there was a car, and behind the others goats!

Once the contestant chose a door, the presenter opened one of the others and let the contestant to change his selection.  Should he change the door he had chosen? What would you do?

Probability is the same for every door, I’d keep my door.

BIG MISTAKE!!! This is because you are thinking with your heart but not with your brain.  I explain in two steps:

STEP ONE

I have three doors and I have to pick one of them.  As everybody knows the probability of each door to have the car behind is the 33.33% (1 in 3).

Once I picked my door I know the probability of having the car behind my door is 33.33% and the probability that the car is behind one of the other doors is 66.66%

STEP TWO

Then the presenter opens a door with a goat, what is the new situation?

The probability of my door keep the 33.33%, HOWEVER, the probability of the other door rises to 66.66% because probabilities keeps in the same way.  I mean, the probability of having a car behind one of the other doors is 66.66%, as I know one of them, probability still is 66.66% but now all percentage is in one door!!

So thinking in terms of probability, the best decision is to change the door and pick the other.  Of course we are speaking of probabilities, victory is not guaranteed but probability goes from 33.33% to 66.66%

If you don’t trust me try at home.  Take a deck of cards and choose three cards, two black and one red.  Now ask your partner to choose one trying to get the red one, put the back side up of one of the other and offer the chance to change his/her selection.  If he/she doesn’t change he/she will lose a lot of times. 

Repeat the game 20 times and check the results!!

Conclusion

If you ever go to a TV program or you are in a similar situation, ALWAYS change your selection.  Forget about hunch, favorite numbers or whatever.  But please, if you lose don’t ask me for compensation!!