# Kaboobly Cannon

A machine fires its first shot and hits the target, but it misses its second shot.

All its subsequent shots have a probability of hitting the target equal to the proportion of targets hit beforehand. For example, if it hits 5 out of the first 8 shots, then the $$9^\text{th}$$ shot has a probability of $$\dfrac58$$ to hit the target.

What is the probability that it hits exactly 50 out of its first 100 shots?

If the probability can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, submit $$a+b$$.

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