trawler is about to fish in territorial waters of a neighboring country
Source: Polish MO Finals 1976 p5
August 23, 2024
combinatoricsprobability
Problem Statement
A trawler is about to fish in territorial waters of a neighboring country, for what he has no licence. Whenever he throws the net, the coast-guard may stop him with the probability , where is a fixed positive integer. Each throw brings him a fish landing of a fixed weight. However, if the coast-guard stops him, they will confiscate his entire fish landing and demand him to leave the country. The trawler plans to throw the net times before he returns to territorial waters in his country. Find for which his expected profit is maximal.