Question

What is Bayes Theorem?

Answer 1

Bayes theorem:

The conditional probability of one event based on the occurrence of another event is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

If $A$and $B$are two events,

$\mathit{P}\left(A|B\right)\mathbf{=}\frac{\mathbf{P}\left(A\right)\mathbf{P}\left(B|A\right)}{\mathbf{P}\left(B\right)}$

where, $P\left(A|B\right)=$probability of $A$given $B$is true

$P\left(B|A\right)=$probability of $B$given $A$is true

$P\left(A\right),P\left(B\right)=$Independent probability of $A$and $B$

• Bayes' Theorem helps to update the predicted probabilities of an event.
• It is usually implemented in finance in calculating or updating risk evaluation.
• It is a useful element in the implementation of machine learning.