# The importance of updating data

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In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

An entomologist spots what might be a rare subspecies of beetle, due to the pattern on its back.

Hence the knowledge that the item selected was defective enables us to replace the prior probability P(A The interpretation of Bayes’ theorem depends on the interpretation of probability ascribed to the terms. In the Bayesian (or epistemological) interpretation, probability measures a “degree of belief.” Bayes’ theorem then links the degree of belief in a proposition before and after accounting for evidence.

For example, suppose it is believed with 50% certainty that a coin is twice as likely to land heads than tails.

If the coin is flipped a number of times and the outcomes observed, that degree of belief may rise, fall or remain the same depending on the results.

For proposition A and evidence B, In the frequentist interpretation, probability measures a “proportion of outcomes.” For example, suppose an experiment is performed many times.

Even if an individual tests positive, it is more likely that they do not use the drug than that they do. Even though the test appears to be highly accurate, the number of non-users is large compared to the number of users.

The number of false positives outweighs the number of true positives.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.

When applied, the probabilities involved in Bayes' theorem may have different probability interpretations.

The three machines account for different amounts of the factory output, namely 20%, 30%, and 50%.

The fraction of defective items produced is this: for the first machine, 5%; for the second machine, 3%; for the third machine, 1%.

Then, we are given the following information: Given that the item is defective, the probability that it was made by the third machine is only 5/24.

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