**Game Show Problem(Old One)**You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats, if you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open, what should you do?

**For Solution**: Click Here

i will kill him

ReplyDeletestick to your decision.

ReplyDeletethe apopriori probabilities do not change. So stick with the decision

ReplyDeleteStick to your decision, because the probablity of you winning will decrease if you make a new choice again .

ReplyDeletestick to my first answer

ReplyDeleteChange your answer. Even better watch 21 :p

ReplyDeleteTo all comments who say stick to it, you are incorrect. You want to change your decision. The initial decision has a 1 in 3 shot of being correct. Changing to the alternate door has a 2/3 chance of being correct. Think of it this way, if your initial pick is not the car (which has a 2/3 probability) then it must be that the alternate unopened door IS the car.

ReplyDeleteThis is also known as the Monty Hall Problem.

The only reason why the presenter will not open the door you have pointed is because you have pointed to the correct door. The presenter has intentionally confused you by opening a wrong door.

ReplyDeleteIt's better to change ur decision

ReplyDeleteBetter change the decision ..atleasty maths says so.. probablity will increase from 1/3 to 2/3

ReplyDeleteI will not change my selection based on the following logic:

ReplyDeleteIf I would have selected the wrong door, the show anchor would have opened my selected door without any delay to prove me wrong. Since, he has shown me the other door, he wants me to change my choice which I wont.

Hi Khawar

ReplyDeleteIf u talk abt probability better switch the decision

Well it does not matter whether you change the decision or not.

ReplyDeleteInitially the probability of picking the Car = 1/3.

Now that the presenter has shown another door with goat behind it.. Now comes a new scenario.

There are 2 doors with goat and car behind each.

P(picking a goat) = P(picking a Car) = 1/2 irrespective of whether you retain your choice or change it !

If I would have selected the wrong door, the show anchor would have opened my selected door without any delay to prove me wrong. Since, he has shown me the other door, he wants me to change my choice which I wont.

ReplyDeleteSee the starting of movie '21'...

ReplyDeleteWill switch..

Mathematical answer to this question:

ReplyDeleteAnswer: Switch

Consider two scenarios

1st Scenario

- You've picked the right one, the anchor will open a wrong door, so the doors remaining will be correct and wrong, if you change you will get the WRONG one

2nd Scenario

- You've picked the wrong (2nd) one, the anchor will open a wrong door, so the doors remaining will be correct and wrong, if you change you will get the RIGHT one.

3nd Scenario

- You've picked the wrong (3rd) one, the anchor will open a wrong door, so the doors remaining will be correct and wrong, if you change you will get the RIGHT one

It just says that changing your answer will give you 2/3 chance and retaining your answer will give you 1/3 chance

- Jasper :)

Bro i dnt think wat u hav answered is correct bcoz der are 2 possiblities in ur first case dat is the correct one !

Deletethey are as follows

if 1st is shown and the 2nd door is wat u hav picked and is right one !

if 3rd is shown and the 2nd door is wat u hav picked so the probability according to ur answer ll be 50 & 50

You definitely switch. They covered this on Mythbusters and changing your pick gives you a 67% chance of winning. One thing the question didn't fully explain is that the host will ALWAYS open one door with a goat behind it that wasn't your pick and then give you the option to change your pick. So if you pick door 1 there is a 33% chance it is behind that door. There is a 67% chance it is behind door 2 or 3. Since the host HAS to show you a door that has a goat behind it and he cannot pick door 1, the odds are that the prize are behind the door he does not choose are 67%. Therefore you should change your pick to that door.

ReplyDeletei wud say to alw me to choose all 3

ReplyDelete