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Yeah, the scenario is often stated ambiguously. The important points: 1) The prizes are placed behind the doors before the game begins. 2) The host will open
by goto11 5y ago
Yeah, the scenario is often stated ambiguously. The important points:
1) The prizes are placed behind the doors before the game begins.
2) The host will open a door regardless of whether the contestant have selected the door with the prize or not.
3) The door to open is always selected from the remaining doors. The host will never open the door the contestant selected.
4) The door is not selected at random. The host knows where the prize is, and will only open a door without a price.
The counter-intuitive part is not the probabilities, it is the rules the host operates. Some of the rules (2,3) depends on the host not knowing or ignoring where the prize is, while some (4) depend on the host using the knowledge of where the prize is.
- galaxyLogic 5y agoThe trick is that it looks like the host is doing the same thing as you, choosing one of the remaining doors. That trick us into thinking the host is operating under the same rules as the guest, it is like a game and in a game typically all players have to follow the same rules. So it is natural to assume this is so. The situation would be perhaps easier to understand correctly if the host didn't open a door, but told you "I can guarantee to you the car is NOT behind this door"