Quote:
Originally posted by chodadog
Woj; What you are forgetting is that there are two possible box changes if the correct box is initially chosen whereas there is only one possible change if each of the incorrect boxes is initially chosen. So there are 4 possible outcomes for each prize location, for a total of 12 possibilities.
So look. Here are all the possible occurences if the prize is in box A.
Contestant Chooses: Box A
Removed: Box B
Possible Outcomes: Stays/Wins, Switches/Loses.
Contestant Chooses: Box A
Removed: Box C
Possible Outcomes: Stays/Wins, Switches/Loses.
[i]Below: Box A obviously can't be removed because it's the winning box.
Contestant Chooses: Box B
Removed: Box C
Possible Outcomes:Stays/Loses, Switches/Wins.
Contestant Chooses: Box C
Removed:Box B
Possible Outcomes:Stays/Loses, Switches/Wins.
2 wins for switching.
2 wins for staying. [/B]
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You're making a huge mistake by counting both the "contestant chooses A" options as options of similar size as the other two.
By that reasoning, if no boxes were removed and no choice to switch was given, option A would somehow have a 50% chance all by itself.