# Problem 2

# How many passengers to screen?

**Due**: January 19

**Points**: 2

In the "airplane bomber" scenario, we are assuming that:

- There are 200 passengers total.
- At least 20 passengers must collude to make a bomb.
- At least 999 out of 1000 times, not a single passenger will have any bomb-making liquid.

With this in mind, we came up with the following randomized algorithm:

- Randomly choose n passengers to screen.
- If none of the n has any bomb liquid, let the plane fly.
- If
any oneof the n has any bomb liquid, check all 200 passengers.

Determine the number of passengers n that must be screened in order to ensure that the probability that the plane is successfully bombed is less than one in a million. Try to make n as small as possible. Show your work!