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Statistics – Probability Bayes Theorem

One of the most significant developments in the probability field

has been the development of Bayesian decision theory which has

proved to be of immense help in making decisions under uncertain

conditions. The Bayes Theorem was developed by a British

Mathematician Rev. Thomas Bayes. The probability given under

Bayes theorem is also known by the name of inverse probability,

posterior probability or revised probability. This theorem finds

the probability of an event by considering the given sample

information; hence the name posterior probability. The bayes

theorem is based on the formula of conditional probability.

conditional probability of event ${A_1}$ given event ${B}$ is

Similarly probability of event ${A_1}$ given event ${B}$ is

Where

times P (B/A_1) + P (A_2) times P (BA_2) }$

${P(A_1/B)}$ can be rewritten as

(B/A_1) + P (A_2) times P (BA_2)}$

Hence the general form of Bayes Theorem is

times P (B/A_i)}}$

Where ${A_1}$, ${A_2}$…${A_i}$…${A_n}$ are set of n mutually

exclusive and exhaustive events.

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