A multiple choice exam has ten questions. Each question has five possible answers, of which one is correct. Suppose that a student did not s

Question

A multiple choice exam has ten questions. Each question has five possible answers, of which one is correct. Suppose that a student did not study for the exam and, as a result, they guess on every question so that the probability of answering any question correctly is 0.20. 19. What is the probability that the student answers exactly 4 questions correctly

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Savannah 3 weeks 2021-10-08T03:17:46+00:00 1 Answer 0

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    2021-10-08T03:18:50+00:00

    Answer:

    8.81% probability that the student answers exactly 4 questions correctly

    Step-by-step explanation:

    For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    A multiple choice exam has ten questions.

    This means that n = 10

    The probability of answering any question correctly is 0.20.

    This means that p = 0.2

    What is the probability that the student answers exactly 4 questions correctly

    This is P(X = 4).

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881

    8.81% probability that the student answers exactly 4 questions correctly

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