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### 11march

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?

1. i will kill him

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

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

5. stick to my first answer

7. To 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.

This is also known as the Monty Hall Problem.

8. 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.

9. It's better to change ur decision

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

11. I will not change my selection based on the following logic:

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.

12. Hi Khawar
If u talk abt probability better switch the decision

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

14. 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.

15. See the starting of movie '21'...
Will switch..

16. Mathematical answer to this question:
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