An airline has collected an i.i.d. sample of 10000 flight reservations and figured out that in this sample 5 percent of passengers who made a reservation did not show up for the flight. They introduce a policy to sell 100 tickets for a flight that can hold only 99 passengers. Bound the probability of observing such sample and getting a flight overbooked.Consider the following process of generating the two samples:

1. We sample 10100 passenger show up events independently at random according to an unknown distribution p
2. And then we split them into 10000 passengers in the collected sample and 100 passengers booked for the 99-seats flight.

Bound the probability of observing a sample of 10000 with 95% show ups and a 99-seats flight with all 100 passengers showing up by following the above sampling protocol. If you do things right, you can get a bound of about 0.0062