# Bay

February 24, 2023

es' Theorem

Bayes' Theorem is a mathematical formula used to calculate the probability of an event given the occurrence of another event. It is named after Thomas Bayes, an 18th century English mathematician and philosopher who is credited with developing the theorem. Bayes' Theorem is used in many areas of science, including artificial intelligence, machine learning, and medical diagnosis.

At its core, Bayes' Theorem is a way of updating the probability of an event given new information. It is based on the idea that past information can be used to predict future events. To illustrate this concept, consider a simple example. Suppose you have a jar of coins and you want to know the probability that the next coin you draw will be heads. Before drawing the coin, you do not know the exact probability of the coin being heads. However, you can use Bayes' Theorem to calculate the probability of the coin being heads given the information that you have already observed.

To use Bayes' Theorem, you must first identify the two events in question. In this example, the two events are drawing a heads and drawing a tails. You then need to identify the prior probability of each event. The prior probability is the probability of each event occurring before any new information is taken into account. In this example, the prior probability of drawing a heads is 0.5, and the prior probability of drawing a tails is also 0.5.

Next, you need to identify the probability of each event given the new information. This information could be anything from the results of previous coin flips to the results of a survey. In this example, suppose that you have observed that the last five coins drawn from the jar were all heads. The probability of drawing a heads given this new information is 0.8. The probability of drawing a tails is 0.2.

Finally, you can use Bayes' Theorem to calculate the probability of each event given the new information. To do this, you multiply the prior probability of each event by the probability of each event given the new information. In this example, the probability of drawing a heads is 0.5 x 0.8 = 0.4, and the probability of drawing a tails is 0.5 x 0.2 = 0.1.

Bayes' Theorem is a powerful tool for calculating the probability of an event given new information. It has applications in many areas of science, including artificial intelligence, machine learning, and medical diagnosis. By understanding Bayes' Theorem and how to use it, you can make more informed decisions and improve your chances of success.

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#### Justin

Author I enjoy designing and curating experiences both virtually and in 3-dimensional reality. I have a Bachelor of Architecture from the Illinois Institute of Technology and currently practice professionally, but I also manage a few other ventures.