A security system contains two independent electronic components, A and B. For any given day, P(A fails)=0.04 and P(B fails)=0.05. If a component does not fail on one day, it works normally on the next day. Assume failures on different days are independent events. Answer the following.
a. Part 1: (i) Find the probability that both components work throughout a single day.
b. Part 2: (ii) Calculate the probability that the system (both components) works without any failure for seven consecutive days.
c. Part 3: (iii) Determine the probability that the first failure (of either component) occurs exactly on the fifth day.