QUESTION:
How can the probability of an Earth swingby reentry accident be so
low?

ANSWER from FAQ on June 3, 1999:
* The Cassini mission has been designed to ensure than an
inadvertent swingby accident does not occur. Mission rules
state that the chance of such an accident occurring must be
less than one in one million. JPL has conducted an in-depth
analysis, which incorporated human error and historical JPL
spacecraft data, to determine the probability of an
inadvertent reentry. This analysis determined that the
probability of an inadvertent Earth reentry is less than one
in one million. This result may be surprising to some people
(at first) since it is difficult to prove that failures of any
system, particularly spacecraft, can be that small. The result
is driven by two factors.
  
* First, for most of the Cassini trajectory it is very hard to
hit the Earth. In fact, until about 50 days before Earth
swingby, the probability of hitting the Earth is much less
than one in one million regardless of the spacecraft failure
(this is because of the vastness of space, the smallness of
the Earth as a target, and the randomness of a spacecraft
failure or micrometeoroid hit leading to a velocity change).
  
* Second, JPL has "biased" the trajectory for Earth swingby.
This scheme further limits the time and events that could
cause inadvertent reentry by eliminating all failures except
those that give the spacecraft the proper velocity magnitude
and direction to impact the Earth. The spacecraft is biased
5,000 kilometers (3,106 miles) or more away from the swingby
altitude (not less than 500 km) for all but about 7 days prior
to the swingby. The navigation accuracy of NASA spacecraft is
better than 20 km. The biasing strategy effects, coupled with
redundant spacecraft system design, built-in fault detection
and correction systems, and controlled operation (via sending
commands to the spacecraft), particularly during the limited
time when failures could cause impact, lead to the exceedingly
small probability of Earth impact.