91Ó°ÊÓ

A and B are disjoint events and \(\Pr \left( B \right) > 0\) .

The conditional probability of the event A given that the event B has previously occurred is given by:

\(\Pr \left( {A\left| B \right.} \right) = \frac{{\Pr \left( {A \cap B} \right)}}{{\Pr \left( B \right)}};\Pr \left( B \right) > 0\;\;\;...\left( 1 \right)\)

SinceA and B are disjoint events, therefore,

\(\left( {A \cap B} \right) = \phi \Rightarrow \Pr \left( {A \cap B} \right) = 0\)

This implies:

\(\Pr \left( {A \cap B} \right) = 0\)

Thus, equation (1) becomes:

\(\begin{aligned}{}\Pr \left( {A\left| B \right.} \right) &= \frac{{\Pr \left( {A \cap B} \right)}}{{\Pr \left( B \right)}}\\ &= \frac{0}{{\Pr \left( B \right)}}\\ &= 0\end{aligned}\)

Therefore, the required value of the given expression is 0.