# How likely an event is to happen? Shifting from Probability Math to common sense Likelihood?

Posted June 17, 2022

on:Mar 20, 2022

# Probability vs. Likelihood

## Difference between Probability and Likelihood.

People tend to confuse between *probability* and *likelihood*, specially the beginners, and many tend to use the two terms interchangeably. In this article I’m going to try to clear la diferencia between these two terms.

# Probability

Probability is simply how *likely* something is to happen. It is attached to the possible results.

Let’s understand this with un ejemplo.

Consider a normal distribución, where mean is μ, and standard deviation is σ. Then the probability of *X* (independent variable on the X axis, versus the **dependent variable (the data) **on the Y axis) falling between *X=x1* and *X=x2* is the **area under the curve of X=x1 and X=x2 (colored red in the above figure).**

Mathematically it can be written as

p(x1 ≤ x ≤ x2 | μ, σ)

read as *“probability of x between x1 and x2 (both inclusive) given the distribution with mean=μ and standard desviación = σ”.*

The first part of the above function (part before |) denotes the **hypothesis.**

Here the hypothesis is that la probabilidad of x lying between x1 and x2. The second part (part after |) denotes the *evidence (or fact). *Here the** evidence is the given distribution (the graph).**

# Likelihood

Likelihood talks about the** model parameters** or** la evidencia** (how the data are distributed).

In likelihood, the datos or the outcome is known and the model parameters or the distribution have to be found.

Consider the following example:

Let’s assume that we have taken the measurement, and the measurement is *X=x0*.

Now, the “likelihood of getting *X=x0 *is the corresponding value on the curve *y0”.*

Mathematically:

L(mean=μ, sd=σ | X=x0) = y0

read as, *“the likelihood of a distribution with mean *μ and *standard desviación *σ, *given, X=x0 is y0”.*

The first part of the above equation (part before |) denotes the *evidence (or distribution). *The second part (part after |) denotes the *hipótesis.*

(**kind of the reverse discover**y)

**To summarize:**

- Probabilities are the areas under a
**fixed**distribution. Mathematically denoted by: p( data | distribution ) - Likelihoods are the y-axis values for fixed data points with different distributions. Mathematically denoted by: L( distribution | data )

I hope this article was able to explain la diferencia between probabilidad and likelihood in a clear and concise manner. Feel free to comment below your pensamientos.

## Leave a Reply