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What is Probability?
It measures the likelihood of possible outcomes in a random experiment for an event. Probability is always a number between 0 and 1, where 0 indicates impossibility and 1 indicates the certainty of an outcome. It is the mathematical branch concerned with numerical descriptions and representations of the likelihood of the occurrence of an event or how likely a proposition is expected to be true.
Statistics heavily uses Probability, so a Probability tutor is an expert in Statistics too.
We can predict the outcome of hardly any events with total certainty in real life. However, we can use the concept of probability to make an informed guess on how likely they are to happen. When we toss a fair coin, the only two possible outcomes are getting a head or a tail. The probability of both the outcomes is 0.5 or ½ each, as both the results are equally likely to occur.
Real-life examples of probability
Many of our observations, forecasts, predictions, and decision-making are based on probability, even though we may not always realize it. Here are some examples where probability is the basis for forecasts, predictions, and analysis in real-life. We can assure you, though, that this is just a tiny snippet of how individuals and organizations use probability in almost every decision they make.
Insurance – Insurers were one of the first to use the concept of probability for business officially. The probability of an event is one of the main criteria for making a policy or calculating the premium amount for the insurance companies. Insurance companies use the theory of probability as the statistical method to predict the odds of possible future outcomes.
Weather Planning – Meteorologists use different instruments, tools, and historical weather data to predict weather changes. For example, the average temperature in a month uses probability concepts.
Sports Strategies – Sports teams and experts factor in historical data, among many other factors, to make strategies and predictions for matches and tournaments. Sports betting companies also use probability to ascertain the odds for sporting events.
Game Theory – It supplements the classical theory of probability and surpasses it as a decision-making framework. It works on the idea that the players control some strategic aspects of decision-making and don’t wholly depend on pure chance.
Card games – Almost all the aspects of almost every card game is partially or fully dependent on probability though some facets in certain games depend on strategy.
Natural disasters – The infrastructure development of specific geographies and areas of a town or a locality depends on the probability of natural disasters in that area.
Probability and statistics
A statistic is either an inferential or a measured value of a parameter or an event. Statistics is the mathematical discipline that employs tools and techniques to arrive at these calculations, including forecasts. Forecasts are where probability plays a significant role in statistics. Probability is the statistic that estimates the chance of different possible results of a random experiment.
Probability is the logic behind uncertainty and the tool to measure it. We don’t limit the use of statistics to only the analysis of historical data. As we go beyond it and make predictions and forecasts for decision-making, the theory of probability and its tools are integral and indispensable for statisticians.
Here is a list of some textbooks for your reference.
A First Course in Probability by Sheldon Ross. Publisher – Pearson
Probability – Theory and Examples by Rick Durrett. Publisher – Cambridge University Press
Probability, Random Variables and Stochastic Processes by Athanasios Papoulis, S. Unnikrishna Pillai. Publisher – McGraw-Hill Europe
Probability Theory – The Logic of Science by E. T. Jaynes, G. Larry Bretthorst. Publisher – Cambridge University Press
Introduction To Probability by Dimitri P. Bertsekas, John N. Tsitsiklis. Publisher – Athena Scientific
Probability and Statistics by Morris DeGroot, Mark Schervish (Pearson Modern Classics for Advanced Statistics Series). Publisher – Pearson
Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik. Publisher – Kappa Research, LLC
Probability Theory: A Concise Course by Y.A. Rozanov – Dover Books on Mathematics. Publisher – Dover Publications
Lectures on Probability Theory and Mathematical Statistics by Marco Taboga. Publisher – CreateSpace Independent Publishing Platform
Introduction to Probability Models by Sheldon M. Ross. Publisher – Academic Press
High-Dimensional Probability – An Introduction with Applications in Data Science by Roman Vershynin (Cambridge Series in Statistical and Probabilistic Mathematics). Publisher – Cambridge University Press