Difference Between Conditional Probability and Bayes Theorem
The difference between Conditional Probability and Bayes Theorem can be understood with the help of the table given below,
| Bayes’ Theorem | Conditional Probability |
|---|---|
| Bayes’ Theorem is derived using the definition of conditional probability. It is used to find the reverse probability. | Conditional Probability is the probability of event A when event B has already occurred. |
| Formula: P(A|B) = [P(B|A)P(A)] / P(B) | Formula: P(A|B) = P(A∩B) / P(B) |
Bayes’ Theorem
Bayes’ Theorem is used to determine the conditional probability of an event. It was named after an English statistician, Thomas Bayes who discovered this formula in 1763. Bayes Theorem is a very important theorem in mathematics, that laid the foundation of a unique statistical inference approach called the Bayes’ inference. It is used to find the probability of an event, based on prior knowledge of conditions that might be related to that event.
For example, if we want to find the probability that a white marble drawn at random came from the first bag, given that a white marble has already been drawn, and there are three bags each containing some white and black marbles, then we can use Bayes’ Theorem.
This article explores the Bayes theorem including its statement, proof, derivation, and formula of the theorem, as well as its applications with various examples.