Save the terrified astrologer!
Once upon a time there was a dictator. An Astrologer forecast something bad for him; so the dictator awarded a death penalty to the astrologer. The latter pleaded for his life , so the dictator gave him a chance to save himself and decreed as follows:"I will allow you to put two white balls and two black balls in any manner you like in two urns without disclosing it to anybody. My executioner will choose one of the urns, dip his hand in to it and take out the ball. if the ball is black, he will cut off your head. If the ball is white , your life is saved. try save yourself,if you can." what would you advice the astrologer to do, in order to give himself the maximum probability of saving his life?
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Think about it logically (yes, it should be in the logic section, not Algebra.) Each urn has a half chance of being chosen. If you put one white and one black in each urn, you still have a 50-50 chance of selecting the black one.
But how big can we make the odds in favor of the white ball? If in one of the urns, there is only a white ball, there is a half chance of it being selcted, and the other three balls only have a 1/6th chance. But one of those balls in white, so overall, the white balls have a 2/3ds chance of being selected.
This is the highest that we can get the odds with the given options. All of the other options do not give you the best odds, and are he therefore wrong.
Sorry this wasn't worded the best, I was just putting "Pen on Paper."