# Death Sentence

Score Points: 4Solvers: 8

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die."

What division of marbles would you do to maximize your chances of survival?

If both should have equal number of white marbles, input that equal number, otherwise input the number of white marbles in the bowl with more white marbles.

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You can put different number of marbles in each bowl. What is the way to maximize your chance for getting a black marble with minimum possible marbles in that bowl?

By putting 1 white marble in bowl 1 and 49 white and 50 black marbles in bowl 2, you straight away have a 50/50 chance of choosing bowl 1 and hence choosing the white marble.
Hence probability of getting a white marble from bowl 1 = 1/2 * 1/1 = 0.5(because probability of picking bowl 1 is 1/2, and in bowl 1, probability of picking the white marble is 1/2)
In bowl 2, we have 49 white marbles and 50 black marbles, i.e. total 99 marbles.
Hence probability of getting a white marble from bowl 2 = 1/2 * 49/99 = 0.24747474 (because probability of picking bowl 2 is 1/2, and in bowl 2, probability of picking the white marble is 49/99)
To get the overall chance of getting a white marble, we just add these two, giving us 0.5 + 0.247474 = .747474
Even if you do not understand the method of calculating probability, I think it is easy to understand that half the time you pick bowl 1 and anyways get to live because it has only 1 white marble. In the other half of the cases, their are 49 white and 50 black balls so you have an almost half chance of picking a white ball. This maximizes your chances of getting a white ball.

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