A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope, just two consecutive let…

Selection of any \(1\) out of \(2\) words \(=\frac{1}{2}\)

ANANTPURTgQPHd|[] (\(9\) letters):

Consecutive pairs are (A,N), (N,A), (A,N), (N,T), (T,P), (P,U), (U,R).

Total = \(7\) and "AN" appears \(2\) times.

P(AN|Anantpur) \(=\frac{2}{7}\)

KANPURTgQPHd|[] (\(6\) letters):

Consecutive pairs are (K,A), (A,N), (N,P), (P,U), (U,R).

Total = \(5\) and "AN" appears \(1\) time.

P(AN|Kanpur) \(=\frac{1}{5}\)

\(\therefore\) Required Probability \(=\frac{\frac{1}{2} \times \frac{2}{7}}{\frac{1}{2} \times \frac{1}{5}+\frac{1}{2} \times \frac{2}{7}}=\frac{\frac{2}{7} \times 5}{\frac{17}{7}}=\frac{10}{17}\)