Propeller Head Plaza

Technical and scientific discussion of amps, cables and other topics.

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Re: I guess I will have to quit

Posted by Don T on October 26, 2006 at 00:20:28:
Here's the table you are looking for -
where R = revealed door
door1 door2 door3
win loseR lose
win lose loseR
lose winR lose
lose win loseR
lose lose winR
lose loseR win
Let's look at randomly revealing a door per our example. The possibilities are
loseR2 loseR3 (this row represents what's missing from your POV)
winR2 loseR3
loseR2 winR3
Clearly there is only a one in 6 chance that the winning door is revealed. And since we know that there is a 1/3 chance that door #1 is a winner then 1-1/6-1/3=1/2 gives the odds of winning if we switch.
I have given you all 6 possibilities that can happen.
I guess it depends one how you want to define possibilities but this conversation is about odds and chance which may be quite different than possibilities.
In your table to fail to account for the fact that only door 2 and door 3 can be randomly revealed. But the truth of matter is that 1/3 of the time door #1 is going to win and we need to take that into account.

Give me rhythm or give me death!