I need to confirm this scenario.

1 - The contestant picks a door with a goat behind it.

2 - The host opens this door and reveals the goat.

3 - The host gives the contestant the chance to pick a new door from the two remaining ones.

4 - contestant picks a new door.

5 - The classic scenario. Do you change the door or stay in the same door?

The probability is the same as the original problem (2/3)?


  • $\begingroup$ In step 2, why would the host reveal that the contestant had chosen a door with a goat? That's not how the Monty Hall game works. $\endgroup$ – littleO Feb 16 '19 at 2:33
  • $\begingroup$ @littleO It appears to deliberately be a variant, judging by the penultimate line. $\endgroup$ – Theo Bendit Feb 16 '19 at 2:42
  • $\begingroup$ How is what you described different from the original Monty Hall problem? $\endgroup$ – Victor S. Feb 16 '19 at 2:44
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    $\begingroup$ @VictorS. It differs in step 2. In the original, Monty opens a different door containing a goat, not the door chosen by the contestant. $\endgroup$ – Theo Bendit Feb 16 '19 at 2:52
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    $\begingroup$ There is something a little ridiculous here. In step 3, the host reveals that the door you picked had a goat behind it. Therefore, it's obvious that you will choose another door - you already know your first choice was wrong. $\endgroup$ – Victor S. Feb 16 '19 at 3:01

If I understand this correctly, the host opens the door that the contestant had chosen initially and reveals it to contain a goat ... after which the contestant picks one of the other two doors ... after which the contestant is given a chance to switch?

If so, it's just 50-50: what we know about the two remaining doors is completely symmetrical, and the prize has to be behind one of them.

  • $\begingroup$ Thanks but I but the next answer was so confusing for me [link]math.stackexchange.com/questions/2955942/… $\endgroup$ – Carlos Mangel Feb 16 '19 at 3:10
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    $\begingroup$ @CarlosMangel I am sure that the person you were talking to in that conversation did not quite understand what you were asking: they thought you were asking about the original Monty Hall problem, but you weren't. in this problem , it's just 50-50 $\endgroup$ – Bram28 Feb 16 '19 at 3:16
  • $\begingroup$ @CarlosMangel Please remember that the "original Monty Hall problem" is so famous that if you ask a question with three doors, two goats, and a car, people will think you mean the original problem unless you explain very clearly how your question is different. (And sometimes they will think you mean the original problem even if you explain the difference.) $\endgroup$ – David K Feb 16 '19 at 14:10
  • $\begingroup$ Thanks to all. 50% in each door $\endgroup$ – Carlos Mangel Feb 16 '19 at 17:43

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