What are some ideas for my math extended essay related to probability?

When considering ideas for a math extended essay related to probability, several fascinating topics come to mind based on my experience and interest in the subject. Here are some personalized suggestions:

Monte Carlo Simulation: Explore how Monte Carlo simulations can be used to solve complex probability problems. You can demonstrate its applications in various fields, from finance to physics, and discuss its accuracy and limitations.

Bayesian Inference: Delve into Bayesian probability theory, highlighting its real-world applications, such as in medical diagnosis or climate prediction. You can discuss how it's different from classical frequentist probability.

Random Walks: Investigate the mathematics behind random walks and their applications in diverse fields, including biology, finance, and physics. Analyze how different types of random walks can model real-world phenomena.

The Gambler's Fallacy: Discuss the psychology and mathematics behind the Gambler's Fallacy, exploring its origins and implications in decision-making and risk management.

Game Theory and Probability: Study the intersection of game theory and probability, focusing on games of chance, strategic decision-making, and their applications in economics and social sciences.

Rare Events and Extreme Value Theory: Investigate the probability distribution of rare events, emphasizing extreme value theory. You can explore its relevance in risk assessment for natural disasters or financial markets.

These ideas offer a starting point for your math extended essay on probability, allowing you to explore various aspects of this intriguing field. Remember to choose a topic that aligns with your interests and has enough accessible resources for in-depth research.

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