A monitoring unit uses 30 identical sensors, each of which works independently with probability 0.98 on any given day. The unit functions correctly on a day only if all sensors work on that day.
Proceed to solve the following with full justification:
a. (i) Compute the probability that the unit functions correctly on a single day.
b. (ii) Find the probability that at least one sensor fails on a given day.
c. (iii) Determine the probability that the unit functions correctly for 100 consecutive days.