Contextualization

Conditional probability is one of the most important and fascinating concepts in mathematics. It plays a crucial role in the study of various phenomena in science, engineering, medicine, economics, computer science, and many other areas. However, despite its evident usefulness, conditional probability is often misunderstood and misapplied. This project aims to address this issue through a deeper understanding of the nature and applications of conditional probability.

Conditional probability is the calculation of the probability of an event occurring, given that another event has already occurred. If the events are independent, then the conditional probability is simply the probability of the event of interest; however, if the events are dependent, then how the event of interest is affected by the first event must be considered.

At its core, conditional probability is about updating beliefs in the presence of new evidence. It is a way to use the information we have to make more informed predictions about what may happen in the future.

Why is Conditional Probability Important?

The ability to calculate conditional probability is one of the most vital skills in many professions today. For example, in medicine, conditional probability is used to determine the probability of a patient having a disease, given a certain symptom. In computer science, it is used in machine learning algorithms to make predictions based on previous data. In economics, it is used to model uncertainties and make predictions about the future behavior of the market.

The future is increasingly being shaped by technologies that rely on conditional probability, such as machine learning, artificial intelligence, data analysis, and forecasting. Therefore, understanding this topic is essential to prepare our students for a world increasingly based on data.

To deepen your studies, we recommend the following sources:

1. Khan Academy: Conditional Probability
2. Brasil, Escola: Conditional Probability
3. YouTube: Ferretto Channel - Conditional Probability

Practical Activity: "Discovering Conditional Probability through Games and Simulations"

Project Objective

The objective of this project is to explore and understand conditional probability in a playful and practical way, using games and simulations. Through this project, students will delve into the concepts and applications of conditional probability and, at the same time, develop skills in teamwork, time management, problem-solving, and creative thinking.

Detailed Project Description

The project consists of creating and implementing a game or simulation that exemplifies situations of conditional probability. The game or simulation will be designed to show how probabilities are affected when we have additional information about an event. In addition, students should write a report detailing the project and present the game or simulation to the class.

For this project, groups should consist of 3 to 5 students and will have one month to complete the task.

Required Materials

Depending on the nature of the game or simulation that students decide to create, the required materials may vary. However, there is a basic list of resources that may be useful:

• Computer with internet access
• Spreadsheet software (e.g. Microsoft Excel, Google Sheets)
• Materials for creating physical games (if chosen by the students)

Detailed Step-by-Step for Carrying Out the Activity

1. Study and Research: Study the concepts of conditional probability using the provided resources and others you find. Research examples of how conditional probability is used in the real world.

2. Game or Simulation Planning: In a group, plan your game or simulation. It should be designed so that players face situations where conditional probability is in action.

3. Game or Simulation Development: Work as a team to develop your game or simulation. Remember, the idea is to make learning about conditional probability fun and interesting.

4. Testing: Test the game or simulation in your group to see if it works as intended and if it really teaches about conditional probability.

5. Report: Students should write a report, as explained in the introduction of this project. The report should contain an introductory section, the development, conclusions, and the bibliography consulted. The report should detail the theory of conditional probability, the description of the game or simulation, the methodology used in the development of the game, and the perceived results in the tests.

6. Presentation: Finally, students will present their game or simulation to the class. Explain the rules of the game and how conditional probability is used. Then, let your classmates play and learn!

Project Delivery

At the end of the project, each group must deliver the developed game or simulation (or a prototype or representation, in the case of an online game for example), along with a written report. The report must comply with the format described earlier in this project. The report should be clear and detailed, explaining the game or simulation, how it relates to conditional probability, the group's learnings, among other relevant aspects.

In addition, students will have the opportunity to present their work to the class, providing a valuable experience of sharing learning.