Baye’s Rule

In Probability theory, we came across some problems in which it is difficult to compute conditional probability directly. To explain this let us consider two events A and B, then their joint probability is given as: \(\begin{eqnarray}P(A,B) = P(A|B)P(B) \label{eqA}\end{eqnarray}\) and we know that: \(\begin{eqnarray}P(B|A) = \frac{P(A,B)}{P(A)} \label{eqB}\end{eqnarray}\) then using \eqref{eqA} and \eqref{eqB} we get: \(\begin{eqnarray}P(B|A) = \frac{P(A|B)P(B)}{P(A)} \label{bayes}\end{eqnarray}\) Equation \eqref{bayes} is called Baye’s Rule and is useful for calculating certain conditional probabilities as in many problems it is difficult to compute P(B|A) directly, hence we use Baye’s Rule to solve such problems. A few examples are given below:...

Assigning Probability and its Building Blocks

This article is in continuation of the previous article: Introduction to Probability As we defined earlier that the Probability is a likelihood of an event which helps us to predict randomness in our design. It is a function that maps an event to a real number. Assigning Probability helps us to understand how mapping is done ? Our goal is to assign probabilities to events in such a way that this assignment represents the likelihood of occurrence of that event. One way to approach this problem is relative frequency approach which says that you perform an experiment large number of...