Monty Hall Question: 3 doors, choose one. After choice, Monty reveals one of two doors remaining that you did?

Question

not choose.

Should you A) keep your current choice or B) change your choice to the other door Monty did not reveal? Why? Proove it.

Answer 1

this is an old probability puzzle

the answer is, choose the other door

when you made your first choice, you were choosing between 3 doors, you had 1 in 3 chance of being correct

monte only had two choices, not three like you did, because he is not going to reveal the door that you chose, and his choice is not random, he knowingly chooses a remaining door that is not the big win

that makes the chance of the unrevealed unchosen door higher

look at it this way

at first there is a 1/3 chance that the goody is behind any door
then you choose (1/3 chance you are right)

monte eliminates a bad choice, now there are only two choices
if you change your choice, you are choosing from the slate that has had a bad one taken out, your chance of the goody is now 1/2.

This is a common probability puzzler and an interesting way to explore some probability concepts.

Answer 2

The answer is B, change your choice. When this answer was given by Marilyn Vos Savant a while ago in Parade Magazine I was so upset that I set up a Monte Carlo simulation to prove her wrong. She was right. This truly illustrates that humans have no 'feel' for statistics. I urge you to set up the simulation yourself so the realization will hit home. Roll a die to determine which door the big prize is behind - 1 or 2 = door A, 3 or 4 for door B, 5 or 6 for door C.
Record this, then roll a die to decide your choice of doors and record that as well. If you chose the same door as the prize, keeping your choice was correct, so write down a K. If you didn't, the correct choice was change, so write down a C.
Do this for 50 trials, or until you get tired of it, and see what you get.

Answer 3

Its a question of probabilities. And the right answer is (B).

I don't have the full proof available, but it goes something like this. When you made the first pick, each door had a 33% chance of being the winner. After one is revealed, the door you did not pick has a 50% chance of being the right one. 50% > 33%. Ya, I know you want to tell me that so, too, does the door you did pick - this is the part of the answer I do not remember.

Answer 4

it fairly is my favourite situation. that's on your maximum suitable pastime to modify doorways. in case you reside along with your door, there's a one million/3 probability which you will win the activities vehicle. in case you turn doorways, there's a 2/3 probability which you will win the activities vehicle. the simplest way of exhibiting how this works is to particularly guess, and artwork in the process the situation. enable's say i'm the host. I placed the vehicle in the back of door one million. one million. in case you go with door one million, then i will open the two door 2 or door 3, to bare a goat. there's a one million/3 threat which you go with door one million in case you reside along with your door, then you definitely win the vehicle. in case you turn doorways, you lose the vehicle. 2. in case you go with door 2, then I ought to open door 3, to bare a goat. there's a one million/3 threat which you go with door 2 in case you reside along with your door, then you definitely lose the vehicle in case you turn doorways, then you definitely win the vehicle. 3. in case you go with door 3, then I ought to open door 2, to bare a goat. there's a one million/3 threat which you open door 3 in case you reside along with your door, then you definitely lose the vehicle in case you turn doorways, then you definitely win the vehicle. upload up each and all of the percentages at the same time Win by way of staying along with your door: door one million (one million/3) + door 2 (0) + door 3 (0) = one million/3 threat Win by way of switching: door one million (0) + door 2 (one million/3) + door 3 (one million/3) = 2/3 threat If I placed the activities vehicle in the different door, the percentages would be an identical. What the contestant has to attain is that the percentages are skewed because of the fact the host makes a unsleeping determination to open a door with a goat. if he opened any door, the probabilites could stay an identical for staying or switching, because of the fact he could desire to open the ferarri door. particularly, in case you go with the activities vehicle, you will lose by way of swithicng, yet once you go with a goat, the probabilties are skewed because of the fact the host is forced to open the door with the different goat, exhibiting you which ones door the activities vehicle is in. everytime you go with a goat, the host has to teach you the place the activities vehicle is. that's a relaxing situation.