# Predicting a Die Roll

Two independent, fair 6 sided dice are rolled. The first die face shows a $$3$$. The second die rolls under the table, so you can not see its face. The probability that the dice under the table is $$3$$ given that the first dice is $$3$$ can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a + b$$?

×