# Difference between prior and posterior

I am not sure why we need posterior probability. Is it same that we say y hat = p(y=1)? If not, what is the difference between these two?

A prior probability simply means what is the probability of y being 1.
A posterior probability means given the data what is the probability of y being 1. It sort of says given the set of x values what is the probability of y being 1. In contrast a prior probability would mean what is the probability of any observation being 1, not the given observation.

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that makes sense. Thank you!

Hi @xz90, and welcome to the DLS Specialization! The term posterior probability is not appropriate here, nor if prior probability. These concepts are part of Bayesian statistics, and are linked through Bayesâ€™ rule. We will not (explictly) apply Bayesian statistics in the Specialization.

The term that you are searching for is conditional probability, appropriate to probability and statistics, writ large (i.e., both frequentist and Bayesian). The highlighted equation is read â€śy-hat equals the probability that y is equal to one conditional on x being equal to x.â€ť The conditioning information x would be, for example, a particular example (e.g. an image).

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Thank you very much! This is very helpful.