A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for

Question

A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly? A.0.236 B.0.764 C.0.00800 D.0.283

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Hadley 5 days 2021-10-13T01:10:40+00:00 1 Answer 0

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    2021-10-13T01:12:22+00:00

    Answer:

    A.0.236

    Step-by-step explanation:

    For each question, there are only two possible outcomes. Either Judy guesses it correctly, or she does not. The probability of Judy guessing 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.

    12 questions

    This means that n = 12

    5 possible answers, only one of which is correct.

    This means that p = \frac{1}{5} = 0.2

    If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

    This is P(X = 3).

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

    P(X = 3) = C_{12,3}.(0.2)^{3}.(0.8)^{9} = 0.236

    So the correct answer is:

    A.0.236

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45:7+7-4:2-5:5*4+35:2 =? ( )