Question

What is the difference between conditional probability and Bayes Theorem?

Answer 1

Difference between conditional probability and Bayes Theorem:

The differences between conditional probability and Bayes Theorem are tabulated as follows:

S. No.	Conditional Probability	Bayes Theorem
1.	Conditional Probability is the probability of occurrence of a certain event, say $A$, based on some other event $B$ which has already occurred.	Bayes Theorem includes two conditional probabilities for the events, say $A$ and $B$.
2.	The equation of conditional probability is: $P\left(A\right|B)=\frac{P(A\cap B)}{P\left(B\right)}$	The equation of Bayes Theorem is: $P\left(A\right|B)=\frac{P\left(B\right|A)\times P(A)}{P\left(B\right)}$
3.	It is used to compute the conditional probability and the events $A$and $B$ are relatively simple.	It is used in Bayesian inference and in models where we are interested in the distribution up to a normalizing factor $P\left(B\right)$
4.	It is used for relatively simple problems	It gives a structured formula for solving more complex problems.

Hence, the differences between conditional probability and Bayes theorem are stated above.