Conce Unknown to a medical researcher, 9 out of 20 patients have a heart problem that will result in death if they receive the test dr

Question

Conce
Unknown to a medical researcher, 9 out of 20 patients have a heart problem that will result in death if they receive the test drug. 8 patients are randomly selected to
receive the drug and the rest receive a placebo. What is the probability that exactly 6 patients will die? Express your answer as a fraction or a decimal number rounded to
four decimal places.

in progress 0
Thu Cúc 3 years 2021-09-03T10:50:09+00:00 1 Answers 13 views 0

Answers ( )

  1. ThanhThu
    0
    2021-09-03T10:51:50+00:00
    Reply

    Answer:

    0.0367 = 3.67% probability that exactly 6 patients will die

    Step-by-step explanation:

    The patients are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

    Hypergeometric distribution:

    The probability of x sucesses is given by the following formula:

    P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

    In which:

    x is the number of sucesses.

    N is the size of the population.

    n is the size of the sample.

    k is the total number of desired outcomes.

    Combinations formula:

    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)!}

    In this question, we have that:

    20 patients means that N = 20

    Sample of 8 means that n = 8

    9 have the heart problem, so k = 9

    What is the probability that exactly 6 patients will die?

    This is P(X = 6).

    P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

    P(X = 6) = h(6,20,8,9) = \frac{C_{9,6}*C_{11,2}}{C_{20,8}} = 0.0367

    0.0367 = 3.67% probability that exactly 6 patients will die

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )