Masters Running

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Monty Hall Sunday Daily - What Door Will You Run To? (Read 46 times)

Dave59


    What if there were 12 equally likely scenarios:

     

    1. Prize is behind A, you choose A, Monty opens B

    2. Prize is behind A, you choose A, Monty opens C

    3. Prize is behind A, you choose B, Monty opens C

    4. Prize is behind A, you choose C, Monty opens B

    5. Prize is behind B, you choose A, Monty opens C

    6. Prize is behind B, you choose B, Monty opens A

    7. Prize is behind B, you choose B, Monty opens C

    8. Prize is behind B, you choose C, Monty opens A

    9. Prize is behind C, you choose A, Monty opens B

    10. Prize is behind C, you choose B, Monty opens A

    11. Prize is behind C, you choose C, Monty opens A

    12. Prize is behind C, you choose C, Monty opens B

     

     

    In cases 1, 2, 6, 7, 11, and 12 you guessed the right one, and should stay there.

    In cases 3, 4, 5, 8, 9, and 10 you guessed a wrong one, Monty showed you the other wrong one, and you should choose the remaining one.

     

    So, by switching, you'll win 1/2 of the time.

     

     


    Marathon Maniac #957

      I love it when you smart folks duke it out.....

      Life is a headlong rush into the unknown. We can hunker down and hope nothing hits us or we can stand tall, lean into the wind and say, "Bring it on, darlin', and don't be stingy with the jalapenos."

      bhearn


        What if there were 12 equally likely scenarios:

         

        But that's not the way it works. Think about it.

         

        First, the prize is randomly placed behind A, B, or C.

        Second, you choose A, B, or C.

         

        This generates 9 equally likely scenarios.

         

        *Then* Monty opens a door with no prize. This happens regardless of which of the 9 scenarios you are in, so gives you no information about which scenario it is. So they are still equally likely. (Also, it makes no difference if you have a door preference and don't choose randomly; you're still right 1/3 of the time.)

         

        This analysis does, however, critically depend on the rules by which Monty operates. We assume that when you choose the correct door, he chooses randomly between the other two doors to open. (If you guessed wrong, he has no choice which door to open.) If instead, he say always opened the rightmost non-prize door, the answer would be different, because his choice does give you information. In that case, if he opens the rightmost remaining door, switching wins 1/2 of the time; if he opens the leftmost remaining door, switching wins 100% of the time.

        bhearn


          twocat, I am still waiting for your response to my puzzle!

          Dave59


             

            But that's not the way it works. Think about it. 

             

            I believed you.  I was just messing around.  But if you would have explained it as 12 possibilities at first I would have believed that too.

             

            Hard to believe I used to know a lot of this stuff and now I know almost nothing.  I was actually taking the first steps down the road to become a certified actuary when someone offered me a programming job (33 years ago this summer).  

             

             

            bhearn


              I was actually taking the first steps down the road to become a certified actuary when someone offered me a programming job (33 years ago this summer).  

               

              Ha, my first programming job was about 33 years ago too.

                I was actually taking the first steps down the road to become a certified actuary when someone offered me a programming job (33 years ago this summer).

                 

                Ha, my first programming job was about 33 years ago too.

                 

                *&^%$# Trainees.  My 1st programming job was 37 years ago.

                 

                Bill

                "Some are the strong, silent type. You can't put your finger on exactly what it is they bring to the table until you run without them and then you realize that their steadiness fills a hole that leaks energy in their absence." - Kristin Armstrong

                stumpy77


                Trails are hard!

                  Wow--did they even have computers that far back?

                   

                   

                  *&^%$# Trainees.  My 1st programming job was 37 years ago.

                   

                  Bill

                  Need a fast half for late fall.  Then I need to actually train for it.

                   


                  MM#209 / JapanJoyful#803

                    If it was Fortran (and another one I forgot), we had to create programs to analyze various data on computer cards 49 years ago in 1965 in statistics classes.

                    "Enjoy yourself. Your younger days never come again." 100yo T. Igarashi to me in geta at top of Mt. Fuji (8/2/87)

                      Wow--did they even have computers that far back?

                       

                       

                      Yep!  Not the "personal" variety, but the big company kind.  Believe it or not I am a second generation coder.  My Dad, who is now 86, worked as a programmer most of his career.

                       

                      Bill

                      "Some are the strong, silent type. You can't put your finger on exactly what it is they bring to the table until you run without them and then you realize that their steadiness fills a hole that leaks energy in their absence." - Kristin Armstrong

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