Neco 2023 Civic Education Question 7

Three independent anti‑corruption mechanisms operate in a government department: internal audit detects 40% of corrupt acts, a citizen whistle‑blower detects 30%, and random inspection detects 25%. Assuming independence, (a) what is the probability that a corrupt act is detected by at least one mechanism? (b) If each detected act results in a penalty equal to five times the amount stolen, and the average amount stolen per act is \(A\) naira, compute the expected unrecovered loss per act. (c) The department wants the expected unrecovered loss to be less than \(50{,}000\) naira. What is the maximum average amount \(A\) that can be tolerated (rounded to the nearest naira)?