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
(a) 0.39
(b) 0.25
(c) 0.11
(d) none of these

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)0.39 \\ P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ =0.25+0.5-0.14 \\ =0.61 \\ P\left(\text{both A and B not happening}\right)=P{\left(A\cup B\right)}^{\text{'}} \\ =1-P\left(A\cup B\right) \\ =1-0.61 \\ =0.39 \end{gathered}$$