Probability is the branch of mathematics that deals with the study of random events and their likelihood of occurrence. It provides a way to quantify and reason about uncertainty, making it an essential tool for decision-making in fields such as statistics, finance, engineering, and science. The foundation of probability theory is based on the concept of sample spaces, events, and probabilities, which are used to model and analyze a wide range of real-world phenomena. Understanding probability is essential for many applications in our daily lives, including predicting the weather, assessing risk, and analyzing data. There are several types of probability:
Classical probability: This is based on the concept of equally likely outcomes. For example, if you roll a fair dice, the probability of rolling a 6 is 1/6, because there are 6 equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Empirical probability: This is based on the relative frequency of an event occurring in a large number of trials. For example, if you flip a coin 100 times and it lands heads 60 times, the empirical probability of the coin landing heads is 60/100, or 3/5.
Subjective probability: This is based on an individual's personal belief or judgment about the likelihood of an event occurring. It is subjective because it can vary from person to person and is not necessarily based on any objective measure.
Axiomatic probability: This is a mathematical approach to probability that is based on axioms (or assumptions) about the probability of events occurring. It allows for the calculation of probabilities using mathematical techniques and is widely used in the field of statistics.
Conditional probability: This is the probability of an event occurring given that another event has already occurred. For example, the probability of rolling a 6 on a dice after rolling a 4 is 1/6, because there are 6 equally likely outcomes (rolling a 1, 2, 3, 5, or 6) given that the first roll was a 4.
