A Practical Guide To Probability And Randomness.

This course provides a comprehensive introduction to the fundamental principles of probability and randomness, equipping you with the tools to understand, predict outcomes, analyze uncertain and make data-driven decisions in situations in various fields. Whether you're interested in data science, finance, engineering, or simply making better everyday decisions, this course will empower you to quantify risk and make informed choices.

We'll explore key concepts such as probability, random variables, and probability distributions, learning how to model and solve problems related to queuing, risk assessment, or predicting outcomes in games of chance like stock market fluctuations, weather patterns, or the spread of infectious diseases. We will also delve into statistical inference, learning how to draw conclusions from data and making predictions based on limited information.

Here are some of the key topics that are in this comprehensive course:

• Basic probability concepts (sample spaces, events, conditional probability)

• Random variables (discrete and continuous)

• Probability distributions (Binomial theorem using Pascal’s triangle)

• Use of tree and vein diagrams to analyze and calculate events.

Let us ,extensively, elaborate the constituents of this course. These include but not limited to modeling chance probability for sequence of outcomes that is use to solve for probability of events, A table of value was created to enable student understand some important terminologies that exist in probability, randomness and simulation to interpret chance behaviour as in the case of randomness which helps in performing simulation on a given trial of samples with explicit examples.

The lecture gives insight on how to find probability of event by applying laws of probability for mutually exclusive events and independent events, general independent rule and using complement rule to simplify the task that is involve in solving time consuming probability problems, interpret and analyze conditional probability of events and other related class of events using two way table, venn diagram and tree diagram.

In the case of venn diagram, set notations are used to connect probability terms with set to maximize the application of probability on other branches of mathematics. Binomial theorem which involved combinatory concept, its derivative from Pascal's triangle, is used to solve questions pertaining probability. There are  multi-choice questions used in the lectures to buttress the ideals behind probability and for the understanding of the course and to ensure that the goal of our students are met with 100% guarantee.

Real-world examples are co-operated in this course and case studies to illustrate the power of probability in diverse applications. Through a combination of lectures in each of the successive sections, problem sets, and interactive exercises, you will develop a strong foundation in probability and randomness and gain the confidence to apply these concepts in your chosen field.