Probability

Question

P( A union B)=.6

P( A intersection B)=.25

Find  P(A`) +P(B`) ?

where P(A`) means probability of A complement.

Answer 1

$\begin{align*} &\Rightarrow P\left ( A' \cup B' \right ) = {\color{red}{P\left ( A' \right ) + P\left ( B' \right )}} - P\left ( A' \cap B' \right ) \\ &\Rightarrow P\left [ \left ( A \cap B \right )' \right ] = {\color{red}{P\left ( A' \right ) + P\left ( B' \right )}} - P \left [ \left ( A \cup B \right )' \right ] \\ &\Rightarrow 0.75 = {\color{red}{P\left ( A' \right ) + P\left ( B' \right )}} - 0.4 \\ &\Rightarrow {\color{red}{P\left ( A' \right ) + P\left ( B' \right )}} = 1.15 \end{align*}$