The file has n line, so the probability of picking the kth line is 1 / k * k / k+1 * … * n-1 / n = 1 / n int k; int i = 1; String s = f.readLine(); //assume at least one line while (true) { String next = f.readLine(); if (next == null) return s; k = random(i + 1); if (k == 0) // 1/k return next; s = next; i++; }