Probability of a letter coming from a city I got this question:

A letter is known to have come either from $\text{TATANAGAR}$ or from $\text{CALCUTTA}$. On the envelope just two consecutive Letters $\text{TA}$ are visible. What is the probability that the letters came from $\text{TATANAGAR}$?

My attempt:
Total number of cases $=3$, as there are three such pairs.
Probability $={{\text{Favourable}}\over{\text{Total}}}=\frac23$
However, the answer is given to be $7\over11$.
How is this possible? Please help.

$$T\equiv \text{comes from Tatanagar}\quad \text{and}\quad C\equiv \text{Comes from Calcutta}\rightarrow \left\{ \begin{array}{lcc}
             p(T)=\dfrac{1}{2} \\
             \\ p(C)=\dfrac{1}{2}
             \end{array}
   \right.$$
$$\text{Possible choices of two consecutive letters:}\left\{ \begin{array}{lcc}
             \text{In TATANAGAR}: 8 \\
             \\ \text{In CALCUTTA}: 7
             \end{array}
   \right.$$
$$\text{Event} D\equiv \text{The chosen couple of letters is TA}\rightarrow \left\{ \begin{array}{lcc}
             p(D|T)=\dfrac{2}{8} \\
             \\ p(D|C)=\dfrac{1}{7}
             \end{array}
   \right.$$
$$p(T|D)=\dfrac{p(T\cap D)}{p(D)}=\dfrac{\frac{1}{2}\cdot \frac{2}{8}}{\frac{1}{2}\cdot \frac{2}{8}+\frac{1}{2}\cdot \frac{1}{7}}=\dfrac{\frac{1}{8}}{\frac{7+4}{56}}=\dfrac{7}{11}$$
