Question

$P ( A )=\frac{4}{5}, P \left( B ^{'}\right)=\frac{2}{5}$ and $P ( A \cap B )=\frac{1}{2}$, then $P \left( A \cap B ^{'}\right)$ equals.

• A. $\frac{2}{7}$
• B. $\frac{1}{5}$
• C. $\frac{3}{10}$
• D. $\frac{1}{10}$
• E. $\frac{2}{5}$

Answer 1

Answer: (C)

$P ( B )=1 -P\left(B^{'}\right)= l -\frac{2}{5}=\frac{3}{5} $
$\because P ( A \cup B ) = P ( A )+ P ( B )- P ( A \cap B ) $
$=\frac{4}{5}+\frac{3}{5}-\frac{1}{2}=\frac{9}{10} $
$\therefore P \left( A \cap B ^{'}\right) = P ( A \cup B )- P ( B ) $
$=\frac{9}{10}-\frac{3}{5}=\frac{3}{10} $