In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 2

Question

In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 22 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they did not complete the homework

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Sophia 3 months 2022-02-02T13:45:11+00:00 2 Answers 0 views 0

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    0
    2022-02-02T13:46:15+00:00

    Answer:

    The probability that a student passed the test given that they did not complete the assignment is [tex]\frac{15}{22}[/tex].

    Step-by-step explanation:

    The probability of an event E is the ratio of the number of favorable outcomes n (E) to the total number of outcomes N.

    [tex]P(E)=\frac{n(E)}{N}[/tex]

    The union of two events is:

    [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

    The intersection of the complements of two events is:

    [tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]

    The condition probability of an event given that another event has already occurred is:

    [tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

    Denote the events as follows:

    A = students who passed the test

    B = students who completed the assignment

    Given:

    N = 27

    n (A) = 17

    n (B) = 22

    [tex]n(A^{c}\cap B^{c})[/tex] = 3

    Compute the value of P (AB) as follows:

    [tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]

      [tex]P(A\cup B)=1-P(A^{c}\cap B^{c})[/tex]

                      [tex]=1-\frac{3}{27}\\[/tex]

                      [tex]=\frac{24}{27}[/tex]

    Compute the value of P (A ∩ B) as follows:

    [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

    [tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]

                   [tex]=\frac{17}{27}+\frac{22}{27}-\frac{24}{27}\\[/tex]

                   [tex]=\frac{17+22-24}{27}[/tex]

                   [tex]=\frac{15}{27}[/tex]

    Compute the value of P (A | B) as follows:

    [tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

                [tex]=\frac{15/27}{22/27}[/tex]

                [tex]=\frac{15}{22}[/tex]

    Thus, the probability that a student passed the test given that they did not complete the assignment is [tex]\frac{15}{22}[/tex].

    0
    2022-02-02T13:46:22+00:00

    Answer:

    17/22

    Step-by-step explanation:

    my teacher said it was the answer

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