Have you ever heard of the term probability? You might have heard of the word probably?! The word probably means as far as one knows or can tell, almost certainly quite similar to probability. Probability is synonymous with possibility. It is a mathematical discipline concerned with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.
Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in the probability distribution, in which you will learn about the possible outcomes of a random experiment. To determine the likelihood of a single event occurring, we must first determine the total number of possible outcomes.
Mathematical Definition of Probability
Probability is a measure of how likely an incident is to occur. Many events are impossible to predict with absolute certainty. Using it, we can only predict the likelihood of an event occurring, i.e. how likely it is to occur. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. Probability for Class 10 is an essential factor for students to understand because it explains all of the fundamental concepts of the subject. The probability of all events in a sample space equals one.
For example, when we toss a coin, we can get either Head OR Tail; there are only two possible outcomes (H, T). However, if we toss two coins into the air, there are three possible outcomes: both coins show heads, both show tails, or one shows heads and one tail, i.e. (H, H), (H, T) (T, T).
Probabilities are classified into three types:
- Theoretical Probability
- Experimental Probability
- Axiomatic Probability
What is Theoretical Probability?
It is based on the likelihood of something occurring. The foundation of theoretical probability is the reasoning behind probability. If a coin is tossed, the theoretical probability of getting a head is 1/2.
What is Experimental Probability?
It is based on the findings of an experiment. The experimental probability can be calculated by dividing the total number of trials by the number of possible outcomes. For example, if a coin is tossed ten times and heads are recorded six times, the experimental probability of heads is 6/10, or 3/5.
What is Axiomatic Probability?
A set of rules or axioms that apply to all types is established in axiomatic probability. These axioms, known as Kolmogorov’s three axioms, were established by Kolmogorov. The axiomatic method to probability quantifies the likelihood of events happening or not happening. This concept is covered in detail in the axiomatic probability lesson, which includes Kolmogorov’s three rules (axioms) as well as various examples.
The likelihood of an event or outcome occurring based on the occurrence of a previous event or outcome is known as conditional probability.
What is Bayes Theorem?
Bayes’ Theorem is a straightforward mathematical formula for calculating conditional probabilities. Bayes theorem plays an important role in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who believe that rational belief is governed by probability laws, use conditional probabilities extensively in their theories of evidence and empirical learning models.
Bayes’ Theorem is crucial to these efforts because it simplifies the calculation of conditional probabilities and clarifies key aspects of the subjectivist position. Indeed, the Theorem’s central insight — that a hypothesis is proved by any body of data that its reality makes it probable — is the foundation of all subjectivist methodology. Do you find the topic probability interesting? You can visit Cuemath to learn more.
Real Applications of Probability
There are numerous real-world applications for probability:
Forecasting the weather: We always check the weather forecast before going on an outing or having a picnic. Assume the forecast indicates a 70% chance of rain. Do you ever wonder where the other 70% comes from? Meteorologists forecast the weather using a specific tool and technique. They examine all of the previous days’ historical databases, which have similar temperature, humidity, and pressure characteristics, and so on.