A radio program has a quiz consisting of $3$ multiple-choice questions, each with $3$ choices. A contestant wins if he or she gets $2$ or more of the questions right. The contestant answers randomly to each question. What is the probability of winning? Express your answer in the form \frac{k}{m}, where k and m are integers, and provide the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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