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Amit is going to guess on all 20 questions of his multiple-choice test. Each question on the test has 4 answer options, and only one is correct. What is the best prediction for the number of questions that Amit will answer correctly? Choose 1 answer: (A) Exactly 5 questions (B) Close to 5 questions but probably not exactly 5 questions (C) Exactly 80 questions (D) Close to 80 questions but probably not exactly 80 questions

Amit is going to guess on all 2020 questions of his multiple-choice test. Each question on the test has 44 answer options, and only one is correct.\newlineWhat is the best prediction for the number of questions that Amit will answer correctly?\newlineChoose 11 answer:\newline(A) Exactly 55 questions\newline(B) Close to 55 questions but probably not exactly 55 questions\newline(C) Exactly 8080 questions\newline(D) Close to 8080 questions but probably not exactly 8080 questions

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Full solution

Q. Amit is going to guess on all 2020 questions of his multiple-choice test. Each question on the test has 44 answer options, and only one is correct.\newlineWhat is the best prediction for the number of questions that Amit will answer correctly?\newlineChoose 11 answer:\newline(A) Exactly 55 questions\newline(B) Close to 55 questions but probably not exactly 55 questions\newline(C) Exactly 8080 questions\newline(D) Close to 8080 questions but probably not exactly 8080 questions
  1. Understand the problem: Understand the problem.\newlineAmit is guessing on a multiple-choice test with 2020 questions. Each question has 44 answer options, and only one option is correct. We need to predict how many questions Amit will answer correctly by guessing.
  2. Calculate probability: Calculate the probability of guessing a question correctly. Since there are 44 answer options and only one is correct, the probability of guessing a question correctly is 11 out of 44, or 14\frac{1}{4}.
  3. Use probability to predict: Use the probability to predict the number of correct answers.\newlineTo find the expected number of correct answers, multiply the probability of getting a question right 14\frac{1}{4} by the total number of questions 2020.\newlineExpected number of correct answers = 14×20\frac{1}{4} \times 20
  4. Perform the calculation: Perform the calculation.\newlineExpected number of correct answers = 0.25×200.25 \times 20\newlineExpected number of correct answers = 55
  5. Interpret the result: Interpret the result.\newlineThe calculation shows that the best prediction for the number of questions Amit will answer correctly is 55. However, since guessing introduces variability, it is unlikely to be exactly 55. The prediction is that it will be close to 55 questions.

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