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Monty Hall Problem Puzzle

Monty Hall Problem Puzzle - 3 September

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Famos Monty Hall Problem Puzzle
Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

For Solution : Click Here

21 comments:

  1. I will stick to my choice as the host is trying to mislead me.

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  2. switch the door,because probability of winning by switching is 2/3 whereas by not switching it is 1/3 .So i will prefer switching the door

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  3. totally depends upon luck ....so wont switch .....

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  4. Definitely not just a matter of luck or a misdirection :)

    1/3 of the time, you've selected the door with the car initially.

    The other 2/3 of the time, the car was behind one of the other two doors. In both of those cases, the host has just narrowed that down to one door for you.

    In summary: If you switch, you'll get a car ~66% of the time. If you stand, that drops to ~33%.

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  5. You better switch

    Your first choice has a 1/3 chance of having the car, and that does not change.
    The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.

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  6. One can look it this way: the chosen door has 2/3 chance that it has goat. By switching, one wins the car with this (2/3) chance. The host opens door having goat out of the remaining two doors. He is not doing so randomly he knows which two have goat. If not switched the original 1/3 chance that the chosen door has car still holds.

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  7. Replies
    1. click on
      For Solution : Click Here

      link

      Delete
  8. Kill the host, put toxic gas under one door, open both doors. If your initial choice is right, keep it, if not change it.

    ReplyDelete
    Replies
    1. Actually both not one door.

      Delete
  9. I agree with the swith and here's why:

    The initial probability of choosing the car on the first try is 1 out of 3 or simply 1/3 and like many are saying it is pure luck since each door has an equal probability of having a car.

    Another way to say this is that the intial probability of you choosing a goat when trying to pick the car is 2 out of 3 or simply 2/3. Meaning that you probably picked the goat on the first pick.

    Since the host then proceeds to open another door to reveal the only other goat, everytime you initially pick a goat and then switch you will win a car.

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  10. why would the probability go to one door , and not spread out equally between the 2 doors at this point ?it would seem to me it would be 50/50

    ReplyDelete
    Replies
    1. The 2 doors you didn't pick have a probability of 2/3 of containing a car and a goat (1/3 probability of containing 2 goats). Monty knows which door has the goat and opens it, so there's a 2/3 chance that the door he didn't open contains the car

      Delete
  11. initally probability will be 1/3&2/3.

    but after revealing one gate .....condition is changed 50:50 (one goat & one car) no other hidden condition so ..acc to me toss & proceed..

    ReplyDelete
    Replies
    1. No, it's better to switch.
      Switching wins if you initially choose a goat and Monty reveals the other goat (leaving the car in the remaining door).
      The probability of this happening = 2/3 (Prob of 1st picking goat)* 1 (Prob of Monty revealing goat) = 2/3

      Delete
  12. whether to switch or not, depending on how well you can understand the host... you need to read his face - either he want you to switch or not. if he is, you should better stay. if he does not really provoke you to switch, then better to switch the door... should you win the car, the host will lost his job since someone has won the prize... :D

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  13. The answer is it doesnt matter , if the show is cunning as the person chooses the right car if it is on the right ,someone would switch the goat with the car thus making him lose , this is the case with cunningness if not then the chances would be greater changing!!!!

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  15. Best to switch with prob 2/3. Trick in this problem is we only have 3 doors. Imagine we have 1000, player picks 1, host opens 3,4,...,999,1000 with goats. Initial prob is only 1/1000, to switch is 999/1000.

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  16. The host will defenitely open the door with goat.
    case 1: If the door you selected has a goat in it,the host will definitely open the door with a goat.(p=1)
    case 2:If the door you selected has a car in it,the host can open either of the the two doors,since both of them have a goat inside.(So he selects the door with a prob p=0.5)


    ReplyDelete