JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Let E_1 be the event that the letter came from KANPUR and E_2 be the event that the letter came from ANANTPUR. Since the letter is equally likely to come from either city, P(E_1) = P(E_2) = 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|E_1) = 1 5 . In the word ANANTPUR, there are 8 letters, so there are 7 pairs of consecutive letters: AN, NA, AN, NT, TP, PU, UR. The pair AN appears exactly twice. Thus, P(A|E_2) = 2 7 . By Bayes' theorem, the probability that the letter came from ANANTPUR given that AN is visible is: P(E_2|A) = P(E_2) P(A|E_2) P(E_1) P(A|E_1) + P(E_2) P(A|E_2) P(E_2|A) = 1 2 2 7 1 2 1 5 + 1 2 2 7 P(E_2|A) = 2 7 1 5 + 2 7 P(E_2|A) = 2 7 17 35 = 2 7 35 17 = 10 17 Answer: 10 17