Task:
Solve the following problems:
Many vehicles used in space travel are constructed with redundant systems to protect the flight crew and their equipment. In other words, backup systems are included with many vehicle components so that if one or more systems fail, backup systems will assure the safe operation of the given component and thus the entire vehicle.
For example, consider one particular component of the US space shuttle that has n duplicated systems (ie. one original system and n - 1 backup systems). Each of these systems functions independently of the others, with probability of 0.98. This shuttle component functions successfully provided that at least one of the n systems functions properly.
a. Find the probability that this shuttle component functions successfully if n = 2.
b. Find the probability that this shuttle component functions successfully if n = 4.