question_answer

Consider two events A and B such that \[P(A)=\frac{1}{4},\] \[P\left( \frac{B}{A} \right)=\frac{1}{2},\] \[P\left( \frac{A}{B} \right)=\frac{1}{4}\]. For each of the following statements, which is true

I. \[P({{A}^{C}}\text{/}{{B}^{C}})=\frac{3}{4}\]

II. The events A and B are mutually exclusive

III. \[P\,\,(A\text{/}B)+P\,\,(A\text{/}{{B}^{C}})=1\]

A)  I only

B)  I and II

C)  I and III                       

D)  II and III

E)  None of these