Question

Mark the correct alternative in the following question:

\[\text{ Let A and B be two events  . If } P\left( A \right) = 0 . 2, P\left( B \right) = 0 . 4, P\left( A \cup B \right) = 0 . 6, \text{ then }  P\left( A|B \right) \text{ is equal to} \]

Options

• 0 . 8 

• 0 . 5 

• 0 . 3 

• 0

Answer 1

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