I previously wondered about the possibility of predicting events by exclusion and I was convened that this is a sort of 'Gambler's fallacy' my previous example was like this:
Early discovery of diseases help treating them early before complications occur. Suppose I estimate that a disease ,which is rare, occurs in 1% of patients coming to my department,. Among 1000 patients who came to the hospital, I excluded 800 of them ,by doing some cheap diagnostics,. Do the probability change among the rest 200 patients ?
Now I have a problem combining this with the Monty hall problem , So I repeat the question in a Monty hall style :
I have 10 doors,or patients,one of them has the rare disease(gold). Each door has either yes or no. you've select one door as it contains yes (so the probability that your door is correct is 1 in 10). Now Monty will show you that in the rest (9 doors), eight have 'no', will you change your choice? ,i.e. you will insist on your first choice, or move to the other door.