If a teacher assigns homework on the $n$th day, the probability that she will assign homework on the $(n+1)$ th day is $\frac{1}{3}$. If she does not assign homework on the $n$th day, the probability that she will assign homework on the $(n+1)$ th day is $\frac{2}{3}$. If she assigned homework on a Monday then the probability that she will assign homework on the Thursday of the week is

• A

  $\frac{1}{3}$
• B

  $\frac{7}{27}$
• Correct answer
  C

  $\frac{13}{27}$
• D

  $\frac{2}{3}$

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