The transport of neutral particles in an evacuated duct is an important aspect of nuclear fusion reactor design. In one experiment, particles entering through the duct ends streamed unimpeded until they collided with the inner duct wall. Upon colliding, they were either scattered (reflected) or absorbed by the wall (Nuclear Science and Engineering, May 1986). The reflection probability (i.e., the probability that a particle is reflected off the wall) for one type of duct was found to be .16.

a. If two particles are released into the duct, find the probability that both will be reflected.
b. If five particles are released into the duct, find the probability that all five will be absorbed.
c. What assumption about the simple events in parts a and
b is required to calculate the probabilities?