# RS Aggarwal Class 12 Bayes Theorem and its Applications PDF

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### What are Bayes Theorem and its Applications?

Bayes’ theorem is a fundamental concept in probability theory that describes the relationship between the probability of an event occurring and the probability of another event occurring in relation to that event. It is named after Reverend Thomas Bayes, an 18th-century statistician, and theologian who first proposed it.

The theorem can be written in the following form: P(A|B) = P(B|A) P(A) / P(B)

Where:

• P(A|B) is the probability of event A occurring given that event B has occurred (also known as the posterior probability)
• P(B|A) is the probability of event B occurring given that event A has occurred (also known as the likelihood)
• P(A) is the prior probability of event A occurring
• P(B) is the prior probability of event B occurring

Bayes’ theorem allows us to update our beliefs about the probability of an event occurring based on new information. It is particularly useful in decision-making and problem-solving when we have uncertain or incomplete information.

The theorem has a wide range of applications in fields such as statistics, machine learning, natural language processing, medical diagnosis, image recognition, and more. In machine learning, it is used in Bayesian learning algorithms and Bayesian Networks. Natural Language Processing, it is used in text classification, spam filtering, and information retrieval. In medical diagnostics, it is used to calculate the likelihood of a disease based on symptoms and test results.

Ch-30-Bayess-Theorem-and-its-Applications

## RS Aggarwal Class 12 (All Chapters PDF)

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