Probability and Odds

Before we move on to work with logistic regression, we must clearly understand these essential statistical concepts.

Probability

Probability describes the likeliness of some event happening or occurring on a numerical scale between 0 (impossible) and 1 (sure). The higher the probability is, the more likely the event will occur. Tossing a fair coin or rolling a dice and expecting how often we’ll get heads or a certain number on a dice is simply the outcome divided by the total options or possibilities.

In the case of a fair coin, the probability of getting heads or tails is the same, $\frac{1}{2}$ (0.5 or 50% chance). Similarly, for the dice, the chance of getting a certain number is $\frac{1}{6}$.

Odds

The odds of an event represent the ratio of the:

For example:

So, we can write the following:

It’s helpful to think of the numeric odds as a ratio. The following description could be useful to understand how probability and odds are related.

Where $p$ is an event under observation, and $q$ is for all other possible events.

Examples

The following are some examples related to probability and the odds.

• A dice roll of 1 or any number:

  • Probability = ...