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A fair die will be rolled 9 times. What is the probability that 4, 5, or 6 is rolled exactly 2 times? Round your answer to four decimal places.

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  1. Today, 11:16
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    Probability (4,5 or 6) exactly 2 outcomes = 6/54 or 0.1111

    Step-by-step explanation:

    Probability of the die to have, 4, = 1/6

    Probability of the die to have, 5, = 1/6

    Probability of the die to have, 6, = 1/6

    It is rolled 9 times

    Probability that 4 is rolled 2 times out of 9 outcomes = 2/9

    Probability that 5 is rolled 2 times out of 9 outcomes = 2/9

    Probability that 6 is rolled 2 times out of 9 outcomes = 2/9

    Probability of the die to have 4 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

    Probability of the die to have 5 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

    Probability of the die to have 6 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

    Probability that 4,5, or 6 is rolled exactly two times = 2/54+2/54+2/54 = 6/54 = 0.1111
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