If $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are mutually exclusive and exhaustive events of a random experiment such that $P(A)=\frac{2}{3} P(B)$ and $P(B)=2 \cdot P(C)$ then $P(A \cup C)=$

• A

  $\frac{3}{13}$
• B

  $\frac{5}{13}$
• Correct answer
  C

  $\frac{7}{13}$
• D

  $\frac{9}{13}$

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