Question

A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is

Options

• 0.39

• 0.25

• 0.11

• none of these

   

Answer 1

\[ 0 . 39\]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ = 0 . 25 + 0 . 5 - 0 . 14\]
\[ = 0 . 61\]
\[P \text{ (both A and B not happening) } = P \left( A \cup B \right)' \]
\[ = 1 - P\left( A \cup B \right)\]
\[ = 1 - 0 . 61\]
\[ = 0 . 39\]