The word MISSISSIPPI consists of the following letters: M, I, S, S, I, S, S, I, P, P, I.

\(Count of each letter: M = 1, I = 4, S = 4, P = 2.\)

Total number of ways to choose 2 letters from 11: \(\binom{11}{2} = 55\).

Ways to choose 2 identical letters:

• 2 S's: \(\binom{4}{2} = 6\)
• 2 I's: \(\binom{4}{2} = 6\)
• 2 P's: \(\binom{2}{2} = 1\)

Total ways to choose 2 identical letters: \(6 + 6 + 1 = 13\).

Probability that the two letters are the same: \(\frac{13}{55}\).