# Probability vs. Odds: What’s the Difference? (With Examples)

The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

On the other hand, odds are a measure of chance that cannot necessarily be calculated mathematically. The likelihood of an event happening is more of a comparison between the likelihood that it will occur and the likelihood that it won’t, or (chances for): (chances against). It is possible to determine an equation to determine the probabilities of an event happening mathematically if one takes into account total chances as (chances for) + (chances against):

The primary factor to keep in mind when thinking about odds is that they do in fact depend on probability. Although it is not a given that the two have completely different concepts, in terms of construction, one uses probability theory or statistics to calculate odds. In this situation, calculating the likelihood of an event occurring can be done with a simple equation. Consider p as probability:

The concern is not whether an event will occur, but rather how frequently it will occur because probability measures the totality of an event occurring in a total number of events. For instance, one considers how many hearts there are in a conventional 52-card deck when determining how frequently one may draw a heart from a deck of cards:

Summary: 1. Odds are calculated based on the likelihood that an event will ever occur; probability is a mathematical measure of how frequently an event will occur. Odds measure both the chances for and the odds against an event ever occurring, whereas probability only compares the chances that an event will occur against the total number of times it will occur. 3. Probability makes sure that an event will happen, while odds are used to determine whether an event will ever happen.

## What are odds?

### Definition

Odds are a way to compare the number of desired outcomes to the number of undesirable outcomes in order to determine how likely something is to happen. When making frequent predictions, such as in the stock market or other areas of investing, odds calculations can be useful because they can quickly demonstrate how likely an event is to occur by determining whether the number of desired or undesirable outcomes is greater.

Given that odds are frequently expressed as a fraction or ratio to show both sides of a calculation, it is usually possible to tell whether the likelihood of an event occurring is high or low just by looking at the formula.

### Uses

Odds can have many uses across several different industries. In the field of scientific research, specifically in relation to the spread of diseases, one of the most widely used applications of odds occurs. In order to understand how a disease spreads and to develop treatments and responses, scientists can use odds to compare how many people in a population have a disease to how many do not. By determining whether a specific investment might offer a higher risk or return, financial professionals can use odds to assist them in providing financial advice to their clients.

### Formula

You can use this formula to calculate odds:

O = Y / (1 – Y)

The odds formula uses the letters “O” for odds, “Y” for the number of desired outcomes, and a value of 1 for all possible outcomes. As a result, a fraction can be displayed using a condensed version of the formula, with the number of desired outcomes on top and the number of undesirable outcomes below. For instance, the odds formula will produce a fraction of one over one or a one-to-one odds if you want to determine the likelihood that a coin will land on its heads side. This is because there are only two possible outcomes.

## What is probability?

Here are some defining characteristics of probability:

### Definition

Probability is a scale used to express how likely an individual thinks a given event or action is to take place. The number of potential outcomes in a situation and the number of times the desired outcome could possibly occur are the two key factors you can take into account when calculating basic probability. Additionally, there are times when knowing probability can help us make sense of complicated situations, like when a situation has more than two possible outcomes. Typically, probability is expressed as a percentage or a single number between 0 and 1 that can be expressed as a percentage.

### Uses

Professionals can use probability in a variety of ways to inform their predictions and recommendations to clients. Calculating the financial risk or return that a company might experience in a specific market is one frequent application of probability in finance. By calculating the likelihood that an investment will be profitable, financial professionals can use probability to recommend investments that a client might add to their portfolio. Marketers may also use probability to predict how their campaigns will perform in the public based on current trends.

### Formula

The basic probability of one result in a scenario with two possible outcomes can be determined using the formula below:

P(A) = n(A) / n(S)

The probability formula uses the letters “P” for probability, “A” for the desired result, “S” for all possible outcomes, and “n” for the number of times each outcome is actually likely to occur. You can finish the calculation by dividing the total number of possible outcomes by the number of desired outcomes, and then express the result as a decimal or percentage.

For instance, to determine the likelihood that a coin will land on its heads side when flipped, divide the number one, or the number of heads sides, by the number two, or the number of total sides, to obtain a probability of 0. 5 or 50%.

## Probability vs. odds

Odds and probability can diverge in a variety of ways. For instance, odds can be expressed as a fraction or ratio while probability is typically expressed as a percentage. Another distinction is that odds employ a range with no boundaries, whereas probability only uses a range with values between 0 and 1. Additionally, while odds are calculated by comparing the number of desired outcomes to the number of potential undesirable outcomes, probability is calculated by taking into account all possible outcomes of an event.

## Examples of probability and odds

Consider these examples of how to use probability and odds:

### Example 1: Probability

At his workplace, Simon is planning a networking event for businesspeople. Simon wants to hold the event outside, so he wants to know how likely it is that it will rain that day. Simon examines the weather reports from the previous 100 days to determine the likelihood of rain and discovers that rain fell 12 times out of every 100 days. The probability of rain can then be determined by Simon using the probability formula, which might be written as P(rain) = 12 / 100.

Simon as a result learns that there is no chance of rain falling on the day of his event. 12 or 12%.

### Example 2: Odds

This month, Nadia notices that many of her coworkers appear to be suffering from cold symptoms, and many of them end up taking a day off work to get better. Although Nadia has not yet experienced a cold, she is interested in calculating the likelihood that she will based on how many of her coworkers have missed work due to illness over the past month. Nadia’s workplace has 50 employees in total, and she observes that 13 of them have taken a sick day in the previous month and displayed symptoms of a cold.

Nadia can use the odds formula, which might appear as follows: O = 13 / (50 – 13), to determine the likelihood of catching a cold. Nadia learns that based on how many of her coworkers have colds, her chances of getting one are 13/37, or 13:37.

## FAQ

How do you calculate probability vs odds?

Divide the probability by one less than that probability to convert from a probability to odds. So if the probability is 10% or 0. 10 , then the odds are 0. 1/0. 9 or ‘1 to 9’ or 0. 111. Divide the odds by one plus the odds to convert the odds to a probability.

Why do people use odds instead of probability?

A probability must be between 0 and 1 (nothing can happen with a greater than 100% chance). Odds are not so constrained. Odds can take any positive value (e. g. a ⅔ probability is the same as odds of 2/1). Instead, a linear model can be fit using odds (actually, the log of odds, or logit).