Math IA Game of Theory: War Casualties

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Introduction

I have gained valuable skills and knowledge after learning topics on statistics and probability in the syllabus of IB Mathematics Standard Level. However, it has been my desires to come up with an area whereby I can apply the concepts I have learnt in the class to something that was physical and relevant in the world to promote my understanding on the topics. Today, we live in a world where we normally take risks and engage ourselves in many choices where we have to make an important decision. This situation made me think of a current challenge that has emerged between America and North Korea. There has been conflicts and tension that has been developed because of a dangerous test of missiles by North Korea that is capable of destroying many from a far distance.

After revising the topics again, I realized that there must be various actions that both countries can plan to take. As a result, I had to figure out the consequences that would occur when America attack North Korea but North Korea is not attacking America, North Korea attacks America but America is not attacking North Korea and when both countries attack each other. In these situations, we can apply probability to determine the result of each outcome.

Aim of exploration

My main goal in the investigation is applied a probability game that will use Geogebra outside the lesson environment. The analysis will assist in solving an equation that will aid in producing a value that will have to mean in the activities of the world. It will create will solve and provide an answer to the question that is happening today, instead of solving the problems in the syllabus.

Overview of game theory and Probability

Game theory enables us to understand models of mathematics that will involve cooperation and conflict between intelligent rational decision-makers. In this experiment, we will apply real-world challenges of warfare between America and North Korea. On the other hand, the probability is one of the branches of mathematics where the possibility of an event to occur can be evaluated. Numerical measures ranging from 0 and 1 are used in the field of probability. Mostly, 0 is usually used to indicate the impossibility while 1 can be used to highlight the certainty of an event to happen.

In the field of probability, there are various types that describe different events and are applicable. Therefore, my understanding of the concept of probability will help me to analyze and implement the data more efficiently. To begin with, we can represent the situation our case whereby we have two events that cannot occur at the same time. It is either America attacking North Korea but North Korea does not attack America or North Korea attacks America but America does not attack North Korea. We can represent it as disjoint events whereby two events cannot occur at the same time.

Let assume that event A represent America and event B represent North Korea.

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