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KDnuggets’ sister site, **Statology**, has a wide range of available statistics-related content written by experts, content which has accumulated over a few short years. We have decided to help make our readers aware of this great resource for statistical, mathematical, data science, and programming content by organizing and sharing some of its fantastic tutorials with the KDnuggets community.

Learning statistics can be hard. It can be frustrating. And more than anything, it can be confusing. That’s why

Statologyis here to help.

This collection focuses on introductory probability concepts. If you are new to probability, or looking for a refresher, this series of tutorials is right for you. Give them a try, and take a look at the rest of the content on Statology.

**Theoretical Probability: Definition + Examples**

Probability is a topic in statistics that describes the likelihood of certain events happening. When we talk about probability, we’re often referring to one of two types.

You can remember the difference between theoretical probability and experimental probability using the following trick:

- The theoretical probability of an event occurring can be calculated in theory using math.
- The experimental probability of an event occurring can be calculated by directly observing the results of an experiment.

**Posterior Probability: Definition + Example**

A posterior probability is the updated probability of some event occurring after accounting for new information.

For example, we might be interested in finding the probability of some event “A” occurring after we account for some event “B” that has just occurred. We could calculate this posterior probability by using the following formula:

P(A|B) = P(A) * P(B|A) / P(B)

**How to Interpret Odds Ratios**

In statistics, probability refers to the chances of some event happening. It is calculated as:

PROBABILITY:

P(event) = (# desirable outcomes) / (# possible outcomes)

For example, suppose we have four red balls and one green ball in a bag. If you close your eyes and randomly select a ball, the probability that you choose a green ball is calculated as:

P(green) = 1 / 5 = 0.2.

**Law of Large Numbers: Definition + Examples**

The law of large numbers states that as a sample size becomes larger, the sample mean gets closer to the expected value.

The most basic example of this involves flipping a coin. Each time we flip a coin, the probability that it lands on heads is 1/2. Thus, the expected proportion of heads that will appear over an infinite number of flips is 1/2 or 0.5.

**Set Operations: Union, Intersection, Complement, and Difference**

A set is a collection of items.

We denote a set using a capital letter and we define the items within the set using curly brackets. For example, suppose we have some set called “A” with elements 1, 2, 3. We would write this as:

A = {1, 2, 3}

This tutorial explains the most common set operations used in probability and statistics.

**The General Multiplication Rule (Explanation & Examples)**

The general multiplication rule states that the probability of any two events, A and B, both happening can be calculated as:

P(A and B) = P(A) * P(B|A)

The vertical bar | means “given.” Thus, P(B|A) can be read as “the probability that B occurs, given that A has occurred.”

If events A and B are independent, then P(B|A) is simply equal to P(B) and the rule can be simplified to:

P(A and B) = P(A) * P(B)

For more content like this, keep checking out Statology, and subscribe to their weekly newsletter to make sure you don’t miss anything.

** Matthew Mayo** (

**@mattmayo13**) holds a master’s degree in computer science and a graduate diploma in data mining. As managing editor of KDnuggets & Statology, and contributing editor at Machine Learning Mastery, Matthew aims to make complex data science concepts accessible. His professional interests include natural language processing, language models, machine learning algorithms, and exploring emerging AI. He is driven by a mission to democratize knowledge in the data science community. Matthew has been coding since he was 6 years old.