Intuition on why counting is incorrect
When we are counting the number of ways of reaching score >= K and dividing it by the number of ways when score >=K and score <N , we are assuming that the prob
When we are counting the number of ways of reaching ```score >= K ``` and dividing it by the number of ways when ```score >=K and score <N``` , we are assuming that the probability of reaching each of those scores by different paths is the same.\n\nLet\'s say ```W = 10```\nFor example, to reach score 3, we can have multiple paths:\n1, 1, 1\n1, 2\n2, 1\n3\n\nP(1, 1, 1) = 0.1 * 0.1 * 0.1\nP(1, 2) = 0.1 * 0.1\nP(2, 1) = 0.1 * 0.1\nP(3) = 0.1\n\nSo, the probabilities are all different. When we are counting the number of ways of reaching 3, we are ignoring the fact that the probability of reaching it is different by different paths.\n\nHope this gives a slight bit of intuition.
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