You have three doors, behind one there is a prize. You choose door A, after that I ll tell you that behind door B there is no prize, do yuo keep your choice or change it ?
Change it. The probability for door A is 1/3, the probability for the set Door C + Door B is 2/3. The interview adds information on the set stating that Door B prob is 0, so the probability for Door C is 2/3 while Door A stays at 1/3
Balls. Once you know that there is no prize behind door B, prob(B) becomes 0. Then, since the prize must be behind A or C, and you don't know anything about them, prob(A) = prob(C) = 1/2. Any of the doors is OK.
Sorry Filippo (F?) but u r wrong on this one. U may see also it in this way: in the game You ll never be told that your initial choice is wrong, the information added is only about the other two doors. This breaks the symmetry, the probability that your initial choice stays at 1/3 ( It is secluded by the bit of more information added ) , but now the prob of b goes to zero and because all the probabilities must add up to 1, the prob(c) becomes 2/3. I understand it is not intuitive, but not all the math is :)