$\mathrm{A}, \mathrm{B}$ are the events in a random experiment. If $\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{1}{3}, \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4}$, then $\mathrm{P}\left(\frac{\mathrm{A}^{\mathrm{c}}}{\mathrm{B}^{\mathrm{c}}}\right)+\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=$

• A

  $1$
• B

  $\frac{4}{5}$
• Correct answer
  C

  $\frac{11}{8}$
• D

  $\frac{7}{3}$

Hence, the correct answer is option: 'C'.