Refer to the neutral particle transport problem described in Exercise 3.42 (p. 84). Recall that particles released into an evacuated duct collide with the inner duct wall and are either scattered (reflected) with probability .16 or absorbed with probability .84.
a. If 4 particles are released into the duct, what is the probability that all 4 will be absorbed by the inner duct wall? Exactly 3 of the 4?
b. If 20 particles are released into the duct, what is the probability that at least 10 will be reflected by the inner duct wall? Exactly 10?

Data from Exercise 3.42

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.