4 ms·
This is a small enough situation that we can do complete enumeration of the states. Let's say you pick door 1. Let's go through all the possibilities: the stat
by spenczar5 5y ago
This is a small enough situation that we can do complete enumeration of the states.
Let's say you pick door 1. Let's go through all the possibilities: the states of the 3 doors, which one monty reveals, and what do we do, and what is the result?
1 | 2 | 3 || Monty Reveals | You switch | Result
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G | G | C || 2 | Yes | Win
G | G | C || 2 | No | Lose
G | G | C || 3 | N/A | Start Over
G | C | G || 2 | N/A | Start Over
G | C | G || 3 | Yes | Win
G | C | G || 3 | No | Lose
C | G | G || 2 | Yes | Lose
C | G | G || 2 | No | Win
C | G | G || 3 | Yes | Lose
C | G | G || 3 | No | Win
Count 'em up: When you switch, 2 wins and 2 losses. When you don't, 2 wins and 2 losses. Of course, the situation is symmetrical for any starting guess you make.
- mortehu 5y agoWhat would this table look like if Monty always revealed a goat? Would any win or lose row be added or removed? I know the result is right, but I don't think this table illustrates the reason.
- tomerv 5y agoYou are not enumerating the options correctly. You have 3 rows for the GGC and GCG options but 4 for the CGG option, which is assigning the CGG option higher probability. In reality, they have equal weight.
- spenczar5 5y agoAgh, you are right. There should be two “start over” rows in each of GGC and GCG. I can’t write “N/A;” we must say “yes/no” in those. Doesn’t change the result though.