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#11
10-16-2005, 02:14 AM
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Re: Monte hall problem
[ QUOTE ]
The way that I think it is best explained is by looking at all the possible outcomes. Assume the prize is behind door 3 If you never switch the outcomes are: You pick door 1, the host shows you door 2, you stay with door 1. Outcome: lose You pick door 2, the host shows you door 1, you stay with door 2. Outcome: lose You pick door 3, the host shows you door 1 or 2, you stay with door 3. Outcome: win If you always switch the outcomes are: You pick door 1, the host shows you door 2, you switch to door 3. Outcome: win You pick door 2, the host shows you door 1, you switch to door 3. Outcome: win You pick door 3, the host shows you door 1 or 2, you switch to door 1 or 2. Outcome: lose. Therefore by not switching you win 1/3 times. By switiching you win 2/3. [/ QUOTE ] This did it for me, i understood all the other answers, even with that deck or cards and the A of spades i felt like there was evidencee for staying or switching.. but all the outcomes written that way. Top notch, really glad i posted this. Thanks to those that responded. 
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#12
10-18-2005, 07:07 AM
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Re: Monte hall problem
This monte think is starting to get to me [img]/images/graemlins/smile.gif[/img]
[ QUOTE ] The way that I think it is best explained is by looking at all the possible outcomes. Assume the prize is behind door 3 If you never switch the outcomes are: You pick door 1, the host shows you door 2, you stay with door 1. Outcome: lose You pick door 2, the host shows you door 1, you stay with door 2. Outcome: lose You pick door 3, the host shows you door 1 or 2, you stay with door 3. Outcome: win & W If you always switch the outcomes are: You pick door 1, the host shows you door 2, you switch to door 3. Outcome: win You pick door 2, the host shows you door 1, you switch to door 3. Outcome: win & win (!) You pick door 3, the host shows you door 1 or 2, you switch to door 1 or 2. Outcome: lose and lose (!). Therefore by not switching you win 2/4 times. By switiching you win 2/4. [/ QUOTE ] FYP
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#13
10-18-2005, 04:44 PM
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Re: Monte hall problem
I think this a pretty solid explanation. The only thing I would add to those still struggling to see where the 33.3% and 66.7% figures come from is to remember that those are the odds that you'll pick either goat or car (respectively) at the beggining of the experiment when you have three unknown doors to choose from.
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#14
10-18-2005, 08:35 PM
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Re: Monte hall problem
No. The host will pick one or the other. It makes no difference which one. You can't count them as seperate events, because you are not making the descion. The host could always choose to only show you door 1.
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#15
10-19-2005, 07:19 PM
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Re: Monte hall problem
[ QUOTE ]
This monte think is starting to get to me [img]/images/graemlins/smile.gif[/img] [ QUOTE ] The way that I think it is best explained is by looking at all the possible outcomes. Assume the prize is behind door 3 If you never switch the outcomes are: You pick door 1, the host shows you door 2, you stay with door 1. Outcome: lose You pick door 2, the host shows you door 1, you stay with door 2. Outcome: lose You pick door 3, the host shows you another door, you stay with door 3. Outcome: win If you always switch the outcomes are: You pick door 1, the host shows you door 2, you switch to door 3. Outcome: win You pick door 2, the host shows you door 1, you switch to door 3. Outcome: win You pick door 3, the host shows you another door, you switch to the other door. Outcome: lose Therefore by not switching you win 1/3 times. By switiching you win 2/3. [/ QUOTE ] FYP [/ QUOTE ] FYP. You pick door 3 one time out of three. Half of those times, you are shown door one, half you are shown door 2. This means that when you always stay, you win [(0/3)+(0/3)+(1/6)+(1/6)]=1/3 of the time. When you always switch, you win [(1/3)+(1/3)+(0/6)+(0/6)]=2/3 of the time. Therefore, you should always switch.
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