How many passengers to screen?Due: January 19
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 one of 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!