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# Difference Between Probability and Likelihood

Understanding the distinction between likelihood and probability is crucial when working with data. Probability and likelihood are both statistical concepts that are used to estimate the possibility of particular occurrences occurring. Nonetheless, they have various meanings and are utilized in different ways. Probability is the possibility of an event happening based on facts or assumptions that are currently known. The chance of detecting a collection of data given a certain hypothesis or set of parameters is referred to as likelihood, on the other hand. It is important to understand the difference between probability and likelihood because they are used in different ways. Confusing these two notions can lead to mistakes in decision-making and statistical inference.

## What is Probability?

Probability is a measure of the likelihood that an event will actually occur based on information or assumptions that are currently known. The probability of the event is commonly stated as a number between 0 and 1, where 0 indicates impossibility and 1 indicates inevitability.

To determine probability, use the following formula −

$$\mathrm{Probability = Number of favorable outcomes / Total number of outcomes}$$

For instance, the probability of getting heads when flipping a fair coin is 0.5 because there are two possible outcomes (heads or tails), and each outcome has an equal likelihood of occurring.

Probability is used to describe the likelihood of events based on assumptions or to make predictions about the future. For instance, insurance firms determine the chance of a certain occurrence (such as a car accident or a natural disaster) occurring and base their rates on that calculation.

## What is the Likelihood?

The likelihood is a measure of how well a particular hypothesis or model fits the observed data. It refers to the chance of detecting a collection of data, given a certain hypothesis or set of parameters. Finding the set of parameters that increases the likelihood of observing the data is the objective when expressing likelihood as a function of the parameters.

If you were to fit a linear regression model to a collection of data, for example. The likelihood function would gauge how well the model fits the data under observation given a set of parameters (slope and intercept). It is aim to identify the combination of parameters that optimizes the likelihood of detecting the data.

A hypothesis or model is examined using likelihood, and conclusions regarding the underlying factors generating the data are reached as a consequence. It is widely applied in maximum likelihood estimation, a method for identifying the model parameters most likely to have the specified values given a collection of data.

## Probability Vs Likelihood

Probability |
Likelihood |
---|---|

It expresses the likelihood of an event taking place given a certain set of circumstances. |
It describes the likelihood of a set of circumstances in light of an observed event. |

It stands for a number between 0 and 1, where 0 denotes impossible and 1 denotes assurance. |
It is a function of a number of factors rather than having a finite numerical range. |

It can be applied to predict the likelihood of an occurrence occurring frequently in the future. |
You can use it to draw conclusions about the circumstances that contributed to an observed occurrence. |

Using the equation P(event) = (number of positive outcomes) / 2, it can be determined (total number of possible outcomes) |
It can be determined by applying the equation L(conditions) = P(event). |

The calculation needs a set of criteria that are known. |
To compute, a witnessed event is necessary. |

Prior information or presumptions about the situation or circumstances can have an impact. |
It can be impacted by the selection of parameters or presumptions regarding the underlying process. |

It can be employed to figure out what a random variable's anticipated value is. |
It cannot be used to calculate a random variable's anticipated value. |

Once fresh data is gathered, it is utilized in Bayesian statistics to update beliefs. |
To identify the set of circumstances that maximizes the likelihood of the observed data, maximum likelihood estimation is performed. |

## Conclusion

In conclusion, likelihood and probability are two statistical ideas that are similar yet distinct. The probability of an event occurring given a set of assumptions or conditions is known as probability. It has a numerical value and is based on true data. A set of parameters' probability, on the other hand, measures how reasonable they are in light of the observed facts. In spite of not being a probability distribution, it serves as a gauge for the strength of the evidence the data provide. Probability is used to make predictions about future events, whereas likelihood is used to estimate unknown parameters based on seen evidence. Understanding the difference between probability and likelihood is crucial for statistical analysis and modeling as it can assist avoid common misconceptions and errors.