# Come to my birthday party, invitation only!

I invite $$100$$ special friends to my birthday party, who all arrive independently of one another. The arrival times of each person are uniformly distributed between $$07.00\ \text{pm}$$ and $$08.00\ \text{pm}$$. The probability that the $$13$$th person to arrive gets there between $$07.10\ \text{pm}$$ and $$07.30\ \text{pm}$$ is $$\large\color{blue}{p}$$. Find $$\left\lfloor10^{13}\large\color{blue}{p}\right\rfloor$$.

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