The Very Lucky Hijackers

Statistically speaking, the probability of the alleged perpetrators enjoying such a run of luck is vanishingly small. The probability that a mission would succeed can be calculated by estimating the probabilities of achieving each individual task required to fulfill the mission, and then multiplying those probabilities together. (This method of computing probabilities assumes that the individual events are causally independent. Since the success of each task was not strictly independent, the following computation is not statistically rigorous, but is provided only to illustrate a point.)

The following table lists estimates of probabilities for each of several tasks critical to the success of the mission. In all cases we chose much higher probabilities than the facts would warrant, in order to give the official story the benefit of the doubt.
task probability
hijacking Flight 11 1/2
hijacking Flight 175 1/3
hijacking Flight 77 1/4
hijacking Flight 93 1/4
evasion of intercepts by Flight 11 1/2
evasion of intercepts by Flight 175 1/3
evasion of intercepts by Flight 77 1/8
evasion of intercepts by Flight 93 1/8
hitting the North Tower 1/2
hitting the South Tower 1/2
hitting the Pentagon 1/4

Assuming these individual probabilities, the aggregate probability for success in the attack would be:

1/2 * 1/3 * 1/4 * 1/4 * 1/2 * 1/3 * 1/8 * 1/8 * 1/2 * 1/2 * 1/4 = 1/589824

This computation ignores the many other improbable events that worked in favor of the attackers, such as the unprecedented (alleged) crumbling of the steel-framed skyscrapers of the World Trade Center.