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    Question

    Anna is participating in a trivia game with 6 questions,

    each with 3 choices. Only one choice is correct per question. If Anna guesses on all questions, what is the probability that she gets exactly 3 correct?
    A 160/727 Correct Answer Incorrect Answer
    B 170/729 Correct Answer Incorrect Answer
    C 140/729 Correct Answer Incorrect Answer
    D 160/729 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Probability of a correct guess = 1/3 Probability of an incorrect guess = 2/3 Number of ways to choose 3 correct answers out of 6  = (6/3) = 20 So, the required probability = 20 × (1/3)3 × (2/3)3 = (20×1×8)/(27×27) = 160/729

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