Question

Mark the correct alternative in the following question:

\[\text{ If} P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 8 \text{ and } P\left( B|A \right) = 0 . 6, \text{ then } P\left( A \cup B \right) = \]

Options

• \[0 . 24\]

• \[ 0 . 3\]

• \[ 0 . 48 \]

• \[0 . 96\]

Answer 1

\[\text{ We have } , \]
\[P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 8 \text{ and }  P\left( B|A \right) = 0 . 6\]
\[\text{ As, }  P\left( B|A \right) = 0 . 6\]
\[ \Rightarrow \frac{P\left( A \cap B \right)}{P\left( A \right)} = 0 . 6\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 6 \times P\left( A \right)\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 6 \times 0 . 4\]
\[ \Rightarrow P\left( A \cap B \right) = 0 . 24\]
\[\text{ Now } , P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ = 0 . 4 + 0 . 8 - 0 . 24\]
\[ = 1 . 2 - 0 . 24\]
\[ = 0 . 96\]