A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

Step-by-step solution

Let E₁ be the event that the letter came from KANPUR and E₂ be the event that the letter came from ANANTPUR. Since the letter is equally likely to come from either city, P(E₁) = P(E₂) = 1 2 . Let A be the event that the two consecutive visible letters are AN. In the word KANPUR, there are 6 letters, so there are 5 pairs of consecutive letters: KA, AN, NP, PU, UR. The pair AN appears exactly once. Thus, P(A|E₁) = 1 5 . In the word ANANTPUR, there are 8 letters, so there are 7 pairs of consecutive letters: AN, NA, AN