Final answer:
The question pertains to the probability of an incumbent mayor running for re-election and involves applying mathematical concepts to understand electoral processes such as majority elections, where candidates must secure more than 50% of votes.
Step-by-step explanation:
The question relates to the concept of probability in a political context. Specifically, the scenario outlines the probability of an incumbent, the mayor of Mathville, standing for re-election as 1/5, with the deputy running if the mayor chooses not to. This real-world application of probability helps students understand the practical implications of mathematical concepts in the decision-making processes within electoral systems.
In electoral systems, such as plurality and majority elections, the outcomes are determined by different rules. A majority election requires a candidate to secure more than 50% of total votes to win outright, otherwise leading to a runoff if no candidate meets this threshold. Understanding these systems and the probabilities involved allows students to better grasp the electoral process and the chances of various candidates succeeding.