Question

If A and B are two independent events, then write P (A ∩ \[B\] ) in terms of P (A) and P (B).

 

 

Answer 1

\[\text{ A and B are two independent events } .\]
\[ \therefore P\left( A \cap \bar{B} \right) = P\left( A \right)P\left( \bar{B} \right)\]
\[ = P\left( A \right)\left[ 1 - P\left( B \right) \right]\]
\[ = P\left( A \right) - P\left( A \right)P\left( B \right)\]