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Probability : What's it is?

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Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Important terms and meaning 

Probability is a branch of mathematics that deals with the likelihood of an event happening. It can also refer to the quality of being probable or the ratio of favorable outcomes to total outcomes. 

 

Here are some definitions of probability: 

 

Chance

Probability is the chance that an event will occur. For example, there is a 50% probability that an unbiased coin will land on heads. 

 

Ratio

Probability is the ratio of favorable outcomes to total outcomes. For example, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. 

 

Number

Probability is a number between 0 and 1, where 0 means impossibility and 1 means certainty. The larger the probability, the more likely the event is to occur. 

 

Logical relation

Probability can also refer to a logical relation between statements, where evidence that confirms one statement also confirms the other to some degree. 

 

There are different perspectives on probability, including classical, empirical, subjective, and axiomatic. 

In statistics

Here are some terms related to probability in statistics: 

 

Probability: A number that measures how likely an event is to occur. Probabilities can be expressed as fractions between 0 and 1, or as percentages between 0% and 100%. 

 

Classical probability: A type of probability that assumes all possible outcomes are equally likely. For example, when rolling a die, there's a 50% chance of getting an even or odd number. 

 

Statistical probability: Involves collecting, analyzing, interpreting, and displaying data about random events. 

 

Event: A single outcome of an experiment. 

 

Outcome: A possible result of an experiment or trial. 

 

Complimentary event: An event that doesn't happen. 

 

Impossible event: An event that can't happen. 

 

Mutual independence: A collection of events where the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. 

 

When solving probability problems, it's important to carefully read the problem to understand the events and any conditions that might apply. 

Probability: Why an important concept in artificial intelligence?

Probability is an important concept in artificial intelligence (AI) because it helps AI systems make informed decisions: 

 

Probability distribution

A key concept in AI, machine learning, and data engineering, probability distribution helps businesses make informed decisions based on data. It can also be used to create predictive models that can forecast future events. 

 

Probabilistic AI model

This approach incorporates probability distributions and uncertainty into AI systems. It outlines potential outcomes and their likelihoods, which helps AI make informed decisions. 

 

Probabilistic reasoning

A form of knowledge representation that uses probability to indicate the level of uncertainty in knowledge. It's a powerful method for handling uncertainty in AI, and it helps formulate and solve problems in uncertain environments. Probabilistic reasoning uses probability theory to make predictions, draw inferences, and update knowledge based on new data. 

Types of probability terms used in AI : You Should Know

The types of probability used in AI are the following 

Probability 

Classical Probability 

Empirical Probability

Subjective Probability Axiomatic Probability

Conditional probability

Joint probability

Prior probabilities

Distributions

Probability Distribution

Exponential distribution

Multinoulli distribution

Other rules and terms

Bayes' rule

Bayesian inference

Likelihoods

Random variable

Probabilistic graphical models

Mathematical Notation 

The mathematical notation for probability is P(event), which represents the likelihood of an event happening. For example, P(1) represents the probability of getting a 1. 

 

Here are some other mathematical notations for probability:

Pr(A): The probability that an outcome in the event "A" occurs

F(z): Cumulative probability functions

f(z): Probability density functions 

Probability is related to function notation and set theory because the range of possible outcomes of an experiment is a set. A number, called the probability, is assigned to subsets of these outcomes. 

 Formula of probability 

Probability of an Event = Number of Favorable Outcomes / Total Number of Possible Outcomes.

We apply P(A ∩ B) formula to calculate the probability of two independent events A and B occurring together. 

It is given as, P(A∩B) = P(A) × P(B), 

where, 

P(A) is Probability of an event “A” and 

P(B) = Probability of an event “B”

Application's of Probability in AI

Probability is used in artificial intelligence (AI) in a number of ways, including: 

 

Probabilistic reasoning

A key aspect of AI that helps systems make informed decisions when faced with uncertainty or incomplete data. It's used in many AI applications, including machine learning, natural language processing, and robotics. 

 

Quantifying uncertainty

Probabilistic models can quantify the uncertainty associated with predictions, helping users understand how confident the system is in its recommendations. 

 

Mitigating bias

In applications like credit scoring and criminal justice, probability-based models can help identify and correct biased predictions. 

 

Protection from overfitting

Probabilistic models can help prevent overfitting and make coherent inferences from complex data. 

 

Bridging the gap between AI and the real world

Probability can help bridge the gap between AI and the real world, which is inherently uncertain. This can lead to more accurate predictions and more transparent and adaptable AI systems. 

Advantages of Probability 

Probability sampling has several advantages, including: 

 

Representative samples

Probability sampling methods are more likely to produce representative samples that accurately reflect the population's characteristics. 

 

Quantifiable sampling error

Probability sampling allows researchers to estimate sampling error, which can help them calculate confidence intervals and measure the precision of their findings. 

 

Reduced bias

Probability sampling minimizes survey bias, which can help ensure research findings are credible and reliable. 

 

Strong statistical inferences

Probability sampling allows researchers to make predictions and conclusions about the population with a high degree of confidence. 

 

Cost-effective

Probability sampling can be cost-effective because researchers can save money by interviewing a sample subgroup instead of the entire population. 

 

Simple

Probability sampling can provide researchers with simple techniques for assembling and interviewing a randomly drawn subgroup. 

 

Limitations of Probability 

There are a few limitations to probability, including: 

 

Classical approach

This approach is simple and useful for simple examples, but it has limitations when the number of outcomes is infinite, or when the outcomes aren't equally likely. 

 

Frequentist interpretation

This interpretation looks at how often an event occurs after many trials, but it has limitations with infinite repetitions and singular events. 

 

Expected values

These are based on averages and are more useful for repeated decisions than one-off activities. 

 

Probability sampling

This can be time-consuming for large populations, and even with randomization, researchers may end up choosing similar variables that affect data quality. 

Conclusions

Probability is a branch of mathematics that deals with uncertainty and randomness in real-world situations. Here are some conclusions about probability: 

 

Probability is important in daily life

Probability is used in many situations, including political strategy, sports, gaming, insurance, online shopping, and online games. 

 

Probability distributions are important for statistics and data analysis

Probability distributions help people understand and predict the behavior of variables in a system. They also help people make informed decisions and assess risk. 

 

Probability is a numerical measure of likelihood

Probability is a way to measure how likely an event is to occur compared to other events that are not likely to occur. 

 

The story of the distribution is more important than the mathematical expression

When modeling, it's more important to know the story of the distribution than the mathematical expression. 

 

Programming and creating plots of probability distributions is a basic skill

Being able to program and create plots of probability distributions is a basic skill for anyone working in statistics.