# The Bizzare Dice

A die is selected at random from an urn that contains two six-sided dice. Die number $$1$$ has three faces with the number $$2$$ while one face each has the numbers $$1, 3,$$ and $$4$$. Die number $$2$$ has three faces with the number $$4$$ while one face each has the numbers $$1, 2,$$ and $$3$$. The first five rolls of the die yielded the numbers $$2, 3, 4, 1,$$ and $$4$$ in that order. The probability that the selected die was die number $$2$$ can be expressed as $$\,\dfrac{p}{q}$$. Calculate $$\,p+q$$.

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