Black-and-White-Marbles-in-Two-Jars

Suppose there are a large number (>10000), N, of black marbles in a jar. There is an equal number, N, of white marbles in a separate jar.

A quantity, Q, of white marbles are taken out of the jar with white marbles and transferred to the jar with black marbles. The jar with black and white marbles is thoroughly mixed so that the distribution of black and white marbles is uniform.

Afterward, the same quantity of marbles, Q, is taken from the mixed jar of black and white marbles and transferred to the original jar of white marbles to restore the total number of marbles to the original number, N.

What is the expected relationship between the final proportion of white marbles in the white marble jar and black marbles in the black marble jar?

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