5 ms·

The host has to know where the prize is, otherwise how could he open one of the two other doors after the player's first choice?

• LanceH 13y ago
  I've seen it worded poorly where it is stated that contestant picks door 2 and then the host opens door 1 revealing an empty stage. The problem becomes to 50/50 if you change the rules that the host always opens the left most door not picked by the contestant.
  • nbouscal 13y ago
    If the host always opens the left-most door not picked by the contestant, the host would open the door on the prize one out of every three times.
    • Peaker 13y ago
      Indeed, and these cases are the ones we don't examine.
• Peaker 13y ago
  Because it may be that the host opened a random door, which happened not to have the prize in it.
  • nbouscal 13y ago
    If that's the case then you're only examining a subset of the probability distribution, which means you're getting skewed results.
    • Peaker 13y ago
      Yes, and being asked about the nature of these skewed results.