Contextualization

Probability is an area of Mathematics that studies the chances of a certain event happening in a random experiment. It is a powerful tool that helps us understand and predict uncertain behaviors, based on patterns and trends. In this project, we will focus specifically on the concept of dependent events.

Dependent events are those in which the outcome of one affects the probability of the other. For example, when drawing a card from a deck of 52 cards, the probability of drawing an ace is 4/52. If we do not return the card to the deck and draw another one, the probability of drawing an ace on the second draw will be different (3/51), as the total number of cards and the number of aces in the deck have changed.

It is important to highlight that the difference between dependent and independent events is fundamental for the correct calculation of probabilities. Independent events do not affect each other's probability, unlike dependent events. Confusion between these concepts can lead to erroneous decisions based on incorrect probability calculations.

Understanding the concepts of dependent and independent events in Probability is essential in various practical application areas, such as Economics, Engineering, Medicine, among others. It is used to make predictions, make informed decisions, and assess the risks associated with different scenarios.

Furthermore, learning about Probability and dependent events also develops essential skills, such as logical thinking, problem-solving, and critical thinking. These competencies are valuable not only for Mathematics but for various areas of knowledge and life situations.

To delve deeper into the subject, I recommend using the book 'Probability: A Course in Intermediate Level' by Athanasios Papoulis, and the Mundo Educação portal, which has good content on the subject. In addition, Khan Academy offers a complete course on Probability and Statistics, with explanatory videos and practice exercises.

Practical Activity: Operation Deck

Project Objective

The objective of this project is to understand and apply the concept of dependent events in practice, through an experiment with decks of cards. Additionally, it aims to promote collaboration and teamwork.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will receive a deck of 52 cards. The project should be carried out over three weeks, with each student dedicating at least 12 hours to the project.

The experiment will involve drawing cards. Students must document the results, calculate the probabilities, and analyze how they change as the cards are drawn from the deck (dependent event).

Required Materials

• Deck of 52 cards
• Paper and pen to record the results
• Calculator

Detailed Step-by-Step

Step 1: Initial meeting to define the roles of each group member and plan the project execution.

Step 2: Conducting the experiment, which includes drawing cards from the deck and documenting the results. This step should be repeated several times to obtain a significant sample of results.

Step 3: Calculating the probabilities of each event and analyzing how they change as the cards are drawn from the deck. This step should be done together and discussed among all group members.

Step 4: Preparation of a final report documenting the experiments conducted, the probability calculations, and the conclusions drawn. The report should be written according to the provided requirements.

Step 5: Presentation of the project to the class, where each group will share the results and conclusions of their work.

Project Deliverables

At the end of the project, each group must deliver:

• A well-structured final report containing:

  • Introduction with the contextualization and project objectives
  • Development, where the theory of dependent events, a detailed description of the experiment, the methodology used, and the presentation and discussion of the results obtained will be specified
  • Conclusion, summarizing the main points, explaining the learnings obtained, and the conclusions drawn about the project
  • Bibliography used to support the project, which can be books, websites, videos, among others.

• Evaluation of participation and collaboration of group members, to encourage teamwork cooperation.

This practical project complements the theoretical study, providing students with a better understanding of the concept of dependent events in probability and applying them in practice.