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 >>>> >>> >> > > > > > > > > > Yahoo! Groups Links > > > > > > ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
