MathDB
2014 Combinatorics #3: Strings of As

Source:

February 23, 2014
probability

Problem Statement

Bob writes a random string of 55 letters, where each letter is either A,B,C,A, B, C, or DD. The letter in each position is independently chosen, and each of the letters A,B,C,DA, B, C, D is chosen with equal probability. Given that there are at least two A′sA's in the string, find the probability that there are at least three A′sA's in the string.
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