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匿名 發問於 科學及數學數學 · 6 年前

URGENT@@HELP!! 20分

2 個解答

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  • Tony
    Lv 4
    6 年前
    最愛解答

    1.(a)

    the probability that the committee consists of no juniors

    = 9C5 / 15C5

    (ps. 9 freshmen and sophomores, 15 students, 5 picked students)

    = 6/143

    = 0.0420 (3 sig. fig.)

    the probability that the committee consists of no freshmen

    = 11C5 / 15C5

    = 2/13

    = 0.154 (3 sig. fig.)

    1(b) the probability that the committee consists of no juniors and no freshmen

    = 5C5 / 15C5

    = 1/3003

    = 0.000333 (3 sig. fig.)

    1(c)

    Before I teach you how to do this type of question,

    I will talk about the wrong concept that students always have

    wrong concept

    ---------------------------------------------------------------------------------------

    the number of ways of having

    at least one member from each year group in the committee

    = 4C1 * 5C1 * 6C1 * 12C2 = 7920

    the student with this wrong concept commit double counting!!!!

    1: A (freshman), B (sophomore), C (junior), D (freshman), E (freshman)

    2: D (freshman), B (sophomore), C (junior), A (freshman), E (freshman)

    1 and 2 are the same as 1 and 2 are formed by the same people(A,B,C,D,E)

    ---------------------------------------------------------------------------------------

    correct concpet!!!

    ---------------------------------------------------------------------------------------

    The ways of forming a committee:

    (1): all members are from the SAME year group

    (2): all members are from the EXACTLY TWO DIFFERENT year group

    (3): all members are from the (EXACTLY THREE) DIFFERENT year group

    so, the number of ways of having

    at least one member from each year group in the committee

    = all members - (1) - (2)

    = 15C5 - (0 + 1 + 6C5) - (11C5 + 10C5 + 9C5)

    (ps. 11C5: no freshmen, 10C5: no sophomores, 9C5: no juniors)

    = 2156

    ---------------------------------------------------------------------------------------

    the probability that in the committee there is at least one member

    from each year group

    = 2156/3003

    = 0.718 (3 sig. fig.)

    資料來源: have taken a probability course in university
  • 6 年前

    SOR 是1-119/429 =310/429

    2015-01-20 01:36:56 補充:

    我不肯定!!!!!!

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