# Pick White Marble

Probability Level 5

You have 50 white marbles and 50 black marbles, and you are allowed to distribute them as you please in two jars. Then you are blindfolded, pick a jar at random, and a marble from that jar.

Over all possible distributions of the marbles in the two jars, suppose that the maximum value of the probability that the marble picked is white is $\dfrac{m}{n}$, where $m,n$ are coprime positive integers. Find $m+n$.

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