Neco 2018 Geography Question 17

An area experiences an average annual rainfall of 1,200 mm with a standard deviation of 150 mm. The probability of a landslide in a given year is modelled as \(P(L)=0.02\,(R/1000)\), where \(R\) is the rainfall (mm) for that year, provided the average slope exceeds 15°. The area's average slope is 18°. The probability of a flood is \(P(F)=0.03\,(R/1200)\).\n\nAssuming rainfall equals the long‑term mean (1,200 mm) and that landslide and flood events are independent:\n\n1. Compute the original probabilities \(P(L)\) and \(P(F)\).\n2. Determine the probability that at least one of the two hazards occurs in a year.\n\nA mitigation programme reduces the landslide probability by 30 % and the flood probability by 20 %. Re‑calculate the combined probability after mitigation.