Bayes theorem is derived using conditional probability concept then why we need Bayes theorem?
Conditional probability is a useful concept, and Bayes' theorem is a useful tool for making calculations with conditional probabilities.
Bayes' theorem is how to flip conditional probability. If you know P(X|Y) (the probability of X given Y), Bayes' theorem tells you how to calculate P(Y|X).
For example, let's say you want to know the probability of a car accident given that someone is drunk. This itself could be hard to get data for. However, Bayes' theorem tells you how to use the probability that someone is drunk given that they were in a car accident. This is something you can estimate from DUI rates.
They are not the same, it depends on the information you have. Sure, Bayes theorem is derived from conditional probabilities. However, one should not confuse Bayes theorem and Bayes estimation which invokes a deeper investigation.
Conditional Probability is the probability of a certain event (A) based on the occurrence of some other event (B).
P(A|B) = P(A∩B)/P(B)
Bayes theorem is an extension of conditional probability and it helps to use one conditional probability to calculate another one.
P(A|B) = P(B|A) * P(A)/P(B)
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