You are shown two identical bowls in a room – one of them containing 25 white marbles and the other containing 25 black marbles. The marbles are identical to each other other than the aspect of color, of course.
A blindfold person will be brought in to the room and asked to choose any bowl randomly and pick any one marble randomly from that bowl. If it is turns out to be a white marble, you will get a million dollars. If it turns out to be black you get nothing.
However, before the blindfolded person is brought in, you are allowed to mix up all the marbles and place any number of white and any number of black marbles in each bowl. Needless to say, all marbles have to be in one or the other bowl.
How would you place the marbles (meaning how many of which color marbles in which bowl) to give you the maximum chance of winning the million dollars?
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