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    Question

    Maria is taking a quiz that contains 3 questions, each

    with 5 options. Only one option is correct for each question. If Maria guesses all the answers, what is the probability that she will get exactly 2 questions correct?
    A 22/125 Correct Answer Incorrect Answer
    B 19/125 Correct Answer Incorrect Answer
    C 13/125 Correct Answer Incorrect Answer
    D 12/125 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Probability of guessing the right answer for each question = 1/5 Probability of guessing the wrong answer for each question = 4/5 The probability of getting exactly 2 questions correct involves Maria guessing 2 right and 1 wrong. This can happen in (3/2) = 3 different ways So, required probability = 3 × (1/5 × 1/5 × 4/5) = 12/125

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