Airplane Engine Problem: One reason
commercial airplanes have more than one
engine is to reduce the consequences should
an engine fail during flight (Figure 9-7c). Under
certain circumstances, some counterintuitive
things happen when the number of engines is
increased. Assume that the probability that
any one engine will fail on a given flight is 0.1
(this is high, but assume it anyway).
Figure 9-7c
a. For a plane that has four engines, calculate
the probabilities that zero, one, two, three,
and all four engines fail during the given
flight. Show that the probabilities sum to 1,
and explain the significance of this fact.
b. If the plane will keep flying as long as no
more than one engine fails, what is the
probability that the four-engine plane keeps
flying?
c. Suppose a different kind of plane has three engines of the same reliability and that it,
too, will keep flying if no more than one
engine fails. What is the probability that the
three-engine plane keeps flying?
d. Based on your computations in this
problem, which is safer, the four-engine
plane or the three-engine plane?