In this step by step guide, we will walk you through the probability in statistics. We understanding the fundamental concept of probability with theoretical + practical approach to have a better glance of probability with python.
Introduction
Probability is a fascinating branch of mathematics that deals with uncertainty and randomness. it allowing us to make informed predictions and decisions in a wide range of fields. As we can measure it vastness than we can simply put say that from finance to medicine.
If you want to built the concept in probability than you need to understand these factors, that I listed down:
1 — Understanding Probability
Probability measures the likelihood of an event occuring. It ranges from 0 which denotes the impossibility and 1 which denotes the centainty. In quantifying uncertainty, probability enables us to analyze and make decisions based on rational reasoning.
2 — Sample Space and Events
In probability, a sample space refers to the set of all possible outcomes of an experiment. An event is any sunset of the sample space. Let’s take an example to understand that, In flipping a coin, the sample space in (Heads and Tails) and an event can be (Heads) or (Tails).
3 — Assigning Probabilities
If you want to calculate the probability, we assign a number between 0 and 1 to each event in the sample space. For a fair coin
the probability of getting heads or tails is both 0.5 or 1/2.
4 — Probability Rules
- The Sum Rule — For two mutually exclusive events events that cannot happen simultaneously. The probability of either event occuring in the sum of their individual probabilities.
- The Complement Rule — The probability of an event not occurring is equal to 1 minus the probability of the event happenings.
- The Product Rule — For two independent events, events that do not product of their individual probabilities.
5 — Types of Probability
- Marginal Probability — The probability of a single event occurring without considering other events.
- Conditional Probability — The probability of an event happenings given that another event has already occurred.
- Joint Probability — The probability of two or more events happening together.
- Bayes’s Theorem — A formula that helps update the probability of an event based on new evidence.
6 — Probability Distribution
A probability distribution lists all possible outcomes and their corresponding probabilities. In a fair six sided die the probability distribution is (1:1/6, 2:1/6, 3:1/6, 4:1/7, 5:1/6, 6:1/6)
7 — Expected Value
The expected value represents the long term average of a random variable and is calculated by multiplying each outcomes by its
Probability and summing up the results.
8 — Law of Large Numbers
As a number of trials in an experiment increases, the experimental probability of an event approaches the theoretical or actual probability. This principle underlines the reliability of probability based predictions in the long run.
9 — Application of Probability
Probability finds applications in various fields like risk analysis, insurance, gaming, weather forecasting, medical research and decision making.
Conclusion
Probability is powerful tool that empowered us to comprehend uncertainty, make informed choices and understand the world around us. By grasping its fundamental concepts and rules you can unlock a whole new world of insights and applications in both everyday life and professional endeavors. So, embrace the fascinating world of probability and explore its limitless possibilities.
