Neco 2021 Geography Question 45

In a river basin, the probability of a heavy‑rainfall year is 0.20. If heavy rainfall occurs, the probability that the downstream dam fails is 0.05; if heavy rainfall does not occur, the dam failure probability is 0.01. A flood occurs only when the dam fails.\n(a) Compute the overall probability that a flood occurs in a given year.\n(b) If a flood causes an average economic loss of \(\text{₦}150\) million, calculate the expected annual loss without any mitigation.\n(c) An early‑warning system costs \(\text{₦}5\) million per year and reduces flood loss by 30 % when a flood occurs. Determine the expected net annual cost with the system and state whether installing it reduces the expected loss.