I think they mean it's 1 - prob of any person getting sick ** number of people on plane

Any one malfunctioning passenger is sufficient to fail the overall flight. Assume each is independently probable of malfunction. If we know nothing else about the passengers, we can only model them as having some average rate of successful flight without malfunction, say 99.9%.

Say there are 100 passengers. We roll the dice 100 times, once for each passenger.

The success rate for the overall flight would be 0.999 ^ 100 = 90.4% -> About a 10% chance of flight failure.

If there are 400 passengers, we get 67.0%, about a 33% chance of flight failure.

Given enough passengers per flight, few or no flights reach their destination.