What is the difference between conditional probability and Bayes Theorem ?

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Vedantu Content Team · Accepted Answer

Hint:The given questions belong to the concepts of probability. To state out the differences between Bayes Theorem and Conditional Probability, first we must have an idea of their origin. So, Bayes Theorem is a formula that describes how to update the probabilities of hypotheses when given evidence. It follows simply from the axioms of conditional probability, but can be used to powerfully reason about a wide range of problems. And, conditional probability is the probability of one thing given that another thing is true. Also, Conditional Probability is the base concept in Bayes Theorem Complete answer: There are a number of differences between conditional property and Bayes theorem. Some of them are listed in the table below. Conditional ProbabilityBayes TheoremConditional Probability is the probability of occurrence of a certain event, say $A$, based on some other event whether $B$ is true or not. Bayes Theorem includes two conditional probabilities for the events, say $A$ and $B$.The equation of conditional probability is:$P(A|B) = \dfrac{{P(A \cap B)}}{{P(B)}}$The equation of Bayes Theorem is:$P(A|B) = \dfrac{{P(B|A) \times P(A)}}{{P(B)}}$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 $P(B)$It is used for relatively simple problems.It gives a structured formula for solving more complex problems.We know that the Bayes Theorem is derived from conditional probability, but they are further also related, like, if we know the conditional probability, we can use the Bayes rule to find out the reverse probabilities.Note: Bayes' theorem provides a way to revise existing predictions or theories given new or additional evidence. In finance, Bayes' theorem can be used to rate the risk of lending money to potential borrowers. In everyday situations, conditional probability is a probability where additional information is known. Finding the probability of a team scoring better in the next match as they have a former Olympian for a coach is a conditional probability compared to the probability when a random player is hired as a coach. One must know the core concepts of probability to answer such questions correctly.

Conditional Probability	Bayes Theorem
Conditional Probability is the probability of occurrence of a certain event, say $A$, based on some other event whether $B$ is true or not.	Bayes Theorem includes two conditional probabilities for the events, say $A$ and $B$.
The equation of conditional probability is:$P(A\|B) = \dfrac{{P(A \cap B)}}{{P(B)}}$	The equation of Bayes Theorem is:$P(A\|B) = \dfrac{{P(B\|A) \times P(A)}}{{P(B)}}$
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 $P(B)$
It is used for relatively simple problems.	It gives a structured formula for solving more complex problems.