Quote:
Originally Posted by balint-glm
The question is the probability of winning if you switch or not, and the picture I sent above explains this clearly.)
|
No it does not, because the picture shows only 1 of 3 possible variants, in other variant it will be a loss and it will "prove" that changing your mind makes your chances as low as 1/3. Let me quote myself:
Quote:
|
The picture you have posted above it stupid as fuck. The diamond is always in the 1st cup there. Now re-draw it like it's in the 2nd or 3rd cup. And add to it a variant where the opened empty cup was #1, #2 and #3 for each case. You will see that in all cases, the probability to find a diamond under one of 2 remaining cups is 50% and it does not matter if you have changed your mind or not. If you want, I can redraw this picture to "prove" that changing your mind loses 2 times of 3. And you will see that probability of success is not 2/3 but only 1/3 (in fact it's 50%, because (2/3+1/3)/2=0.5). That's in case if you are used to learn math by comics, not by formulas...
|
Your picture and the whole "Monty Hall Problem" works only if the diamond in the 1st cup (we assume it can be in any one of 3, right?). But how it will change if it will be in the 2nd or 3rd one? Try to redraw that stupid picture in your head and you'll see that it does not work anymore
