# Michael's marbles

Two marbles are selected with replacement from a box containing $$R$$ red marbles and $$B$$ blue marbles. If the probability that one marble of each color is drawn is equal to $$\dfrac{15}{32}$$, then the value of $$\dfrac{R}{B} + \dfrac{B}{R}$$ can be expressed as $$\dfrac{a}{b},$$ where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a+b?$$

This problem is posed by Michael T.

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