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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 Ă— (1/5 Ă— 1/5 Ă— 4/5) = 12/125

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