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A multiple-choice quiz consists of \(10\) questions. For each question, there are \(4\) possible answers, only one of which is correct. A student guesses the answer to every question randomly. Let \(X\) be the number of correct answers obtained.
What probability distribution does \(X\) follow? Justify your answer.
Calculate the probability that the student gets exactly four correct answers (round to three decimal places).
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