Statistics for Dummies: 105

5 min readAug 4, 2023

Probability: Definition and Basic Concepts

Introduction

Probability is a measure of the likelihood that an event will occur. The concept of probability originated in the 17th century with the work of mathematician Blaise Pascal and Pierre de Fermat. To calculate probabilities, you need to first understand the basic concepts: sample space, events, and outcomes. Probabilities can be expressed as either fractional or decimal values — the most common format is 50/50 (or 0.5) or 1/2.

Defining Probability: The Study of Random Events

Probability is the study of random events. It is concerned with finding the likelihood of an event occurring, given a set of known conditions and information.

Probability can be applied to any situation where there is uncertainty about the outcome of an event. For example, suppose you want to know how likely it is that your favorite sports team will win its next game against their opponent? Or perhaps you’ve been invited on a blind date and would like some idea as to whether your date will be attractive or not (this may seem like a strange thing for someone who doesn’t like sports or dating). In both cases, we can use probability theory as our guide for making predictions about these situations because both involve randomness at some level — the outcome depends partly on chance rather than being completely determined beforehand by forces outside our control (like destiny).

Understanding Basic Probability Concepts: Sample Space, Event, and Outcome.

The sample space is the set of all possible outcomes. Probability is a number between 0 and 1 that represents how likely it is for an event to occur. In other words, it’s how many times out of a total number n that an outcome will happen. For example:

The probability that you get heads when flipping a coin is 50%, because there are two equally likely possibilities (heads or tails), and one has been chosen as your “outcome.”

In addition to being able to identify an event in terms of its probability, you should also be able to define what constitutes an event based on certain criteria. For example: if we were talking about rolling dice, then any roll with at least one six would be considered an outcome; however if we were talking about drawing cards from a deck without replacement (i.e., once drawn from the deck it cannot be put back), then drawing any ace would not be considered part of our sample space because it cannot happen more than once per draw!

Calculating Simple Probabilities: Finding the Likelihood of an Event.

Calculating Simple Probabilities: Finding the Likelihood of an Event.
The probability of an event is the number of ways that it can occur divided by all possible outcomes.
Since probability is a number between 0 and 1, with 0 meaning impossible and 1 meaning certain, we can use fractions or decimals to describe this relationship. For example: If there are 3 possible outcomes (A, B and C) then we would say that “there is a 1/3 chance” or “the probability” for each outcome individually. When we combine these three possibilities together as one single event though things get more complicated since now there are six possible outcomes instead (ABCABC…). To calculate this type of calculation you need to find out how many different combinations exist within those six categories before you multiply them together as shown below:

Conditional Probability: The Probability of an Event Given Another Event.

The probability of an event A given another event B is the probability that event A occurs, given that we know event B has occurred. It’s calculated by dividing the number of ways in which both events can occur by the total number of possible outcomes.

For example:

Let’s say you’re a poker player and your friend has just told you that he got pocket kings in his last hand (and won). You want to know what this means for your chances at winning against him next time around? The answer lies in conditional probability!

Independent and Dependent Events: Understanding the Relationship Between Events.

In probability theory, two events are said to be independent if their occurrence does not affect each other. For example, if we flip two coins and ask whether or not they both come up heads, this is an example of an independent event. If you know one coin came up heads or tails then that information doesn’t help you predict whether the second coin will come up heads or tails (i.e., it’s still 50/50).

On the other hand, dependent events are those where knowing something about one event affects your knowledge of another event — for example if we flip three coins at once and ask if any combination contains two heads then this would be dependent on whether or not one of those three coins happened to be a tail-side up flip as well!

The Law of Total Probability: An Overview

The law of total probability is a mathematical formula that can be used to calculate the probability of an event, given another event or events. The law of total probability can also be used to find the probability of an event given a second event.

Conclusion

Probability is the study of random events and the likelihood of their occurring. It’s important to understand how probability works because it can help us make better decisions in our everyday lives, such as whether or not we should leave work early on Friday because it will be raining (and therefore unlikely that anyone will drive).

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