Posted on Jun 11, 2016

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:...