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 $\large\color{#3D99F6}{p}$ . Find $\left\lfloor10^{13}\large\color{#3D99F6}{p}\right\rfloor$ .