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