On a multiple-choice test. Abby randomly guesses on all seven questions. Each question has four choices. Find the probability to the n

Question

On a multiple-choice test. Abby randomly guesses on all seven questions. Each question
has four choices. Find the probability to the nearest thousandth, that Abby gets exactly
three questions correct.

in progress 0
Ariana 2 weeks 2021-10-01T10:25:09+00:00 1 Answer 0

Answers ( )

    0
    2021-10-01T10:26:56+00:00

    Answer:

    0.173 probability that she gets exactly three questions correct.

    Step-by-step explanation:

    For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for a question 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.

    Seven questions:

    This means that n = 7

    Each question has four choices.

    Abby guesses, which means that p = \frac{1}[4} = 0.25

    Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.

    This is P(X = 3).

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

    P(X = 3) = C_{7,3}.(0.25)^{3}.(0.75)^{4} = 0.173

Leave an answer

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