No, that's supposed to be true!

(1/2)(1/3) + (1/2)(2/3) = 1/2

Tyson Mao
MSC #631
California Institute of Technology

On Dec 28, 2005, at 4:57 PM, d_j_salvia wrote:

> Hi Bob,
>
> You switched half the time, and won about half the games.
>
> Wasn't that supposed to be false?
>
> Wow! Who woulda thunk it!
>
> Thanks,
>
> David J
>
> --- In [email protected], "Bob Burton" <[EMAIL 
> PROTECTED]>
> wrote:
>>
>> I did 100 trials, swithing my choice for 50 and keeping my choice for
>> the other 50.
>>
>> The results:
>>
>> When keeping choice:  16/50 wins => 32%
>> When changing choice:  32/50 wins => 64%
>> Overall total:  48/100 wins => 48%
>> Conclusion:  You are twice as likely to win if you change your choice.
>>
>> There was obviously a clear distinction between keeping my choice and
>> changing it.
>>
>> I used this to play:
>>
> http://people.hofstra.edu/staff/steven_r_costenoble/MontyHall/ 
> MontyHallSim.html
>>
>> Think of it this way:
>>
>> When you are shown one of the empty doors, your chances of winning by
>> keeping your original choice is still 1/3, not 1/2.  The door shown to
>> you was not chosen at random.
>>
>> ~ Bob
>>
>> --- In [email protected], "d_j_salvia"
>> <[EMAIL PROTECTED]> wrote:
>>>
>>> Hi Duncan and Stefan and Pedro and Evan,
>>>
>>> Sorry, you guys, but you aren't correct.
>>>
>>> In probability there's a thing called the law of large numbers. If  
>>> you
>>> generate a long enough string of numbers "randomly" that eventually
>>> you would have every digit the same number of times. N oparticular
>>> number is favored. Your answer relies upon this law of randomness.
>>>
>>> What is actually wrong with the standard answere you gave is that one
>>> is not dealing with a large number of choices, and, as such, odds *do
>>> not apply.*
>>>
>>> I went to a site with the software and made my choice and did not
>>> switch and I won. Doing it more than once is outside the boundaries  
>>> of
>>> the game.
>>>
>>> Cheers,
>>>
>>> David J
>>>
>>>
>>> --- In [email protected], "Duncan Dicks"
>>> <[EMAIL PROTECTED]> wrote:
>>>>
>>>> I Had a freind who wouldnt believe this no matter how often I
>>> explained the
>>>> maths to him so he set up spreadsheet to test it out.  Very easy to
>>> do and
>>>> confirmed what the maths tells you - you should switch!
>>>>
>>>> Duncan
>>>> ----- Original Message -----
>>>> From: "aznseashell" <[EMAIL PROTECTED]>
>>>> To: <[email protected]>
>>>> Sent: Sunday, December 25, 2005 7:04 AM
>>>> Subject: [Speed cubing group] Re: (Off topic)3 doors...
>>>>
>>>>
>>>> Haven't we had this dicussion before? Or was it in another cubing
>> group?
>>>>
>>>> The game is set up so that if you switch, a winning choice would
>>>> become a losing choice and vice versa. In the beginning you had
> a 1/3
>>>> chance of winning and 2/3 chance of losing. Staying with your choice
>>>> doesn't change your odds of winning (the host will always be able to
>>>> show you a door with nothing behind it no matter which door you
>>>> picked), but switching will turn your probabability of winning
> to 2/3.
>>>>
>>>> If my explanation makes no sense, consider the situation with 100
>>>> doors and one door with a prize. You pick a door, and the host shows
>>>> you 98 doors with nothing behind them. Now it's much more
> obvious that
>>>> you should switch, right?
>>>>
>>>> Shelley
>>>>
>>>>
>>>> --- In [email protected], "richy_jr_2000"
>>>> <[EMAIL PROTECTED]> wrote:
>>>>>
>>>>> It is counter intuitive, but if you are in this situation, your
>>>>> chances would be better to switch to the other door.  It's
> actually
>>>>> quite interesting.
>>>>>
>>>>> -Richard
>>>>>
>>>>> --- In [email protected], Pedro
>>>>> <[EMAIL PROTECTED]> wrote:
>>>>>>
>>>>>> Ok, this is off topic, but is interesting...
>>>>>>
>>>>>>   (please forgive if I make some mistake on the english...)
>>>>>>   Suppose you are at a TV show, where you have 3 doors. 1 of the
>>>>> doors has a car, and the other 2 don't have anything. So, the show
>>>>> presenter asks you to choose a door. So, you choose, but he
> doesn't
>>>>> open your choosen door. He opens an empty door. Then, he makes a
>>>>> question: do you want to continue with your first choice or
>> change to
>>>>> the other door?
>>>>>>
>>>>>>   What do you do?
>>>>>>   What situation gives you more chances of winning?
>>>>>>
>>>>>>   Think about it...
>>>>>>
>>>>>>   Pedro
>>>>>>
>>>>>>
>>>>>> ---------------------------------
>>>>>>  Yahoo! doce lar. Faça do Yahoo! sua homepage.
>>>>>>
>>>>>> [Non-text portions of this message have been removed]
>>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Yahoo! Groups Links
>>>>
>>>
>>
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