The Monthy Hall Problem shows how little intuition humans bear to solve probabilistic enigmas.
Tree doors, one hides a price. The candidate chooses one and then the show master opens another one bearing no price. Would the candidate increase his probability in choosing the leftover door, giving up his first choose?
The astonishing answer: the two doors left (the first-chosen and the remaining-closed) are not of the same probability the price-doors. But the remaining-closed now has a probability of 2/3 in comparison with the first-chosen 1/3.
The trick: the show-master opened a door, given the candidates first choice. in 2/3 of the cases he had to avoid the price-hiding door, indicating that the other bears the price. only if the candidates original try was right, the show-master could open any other door.
I modeled this as BN with GeNie:
The candidate chose State0, the quiz-master showed State1 and the price probability resulted in p(Door0)= 1/3 and p(Door3)= 2/3.
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