星座 發問於 科學及數學數學 · 6 年前

Probability help! Urgent!!!

1)In a factory,there are three light bulb production lines,A,B and C.If a bulb is chose n at random,the probabilities of choosing a bulb produced by production lines A and B are 5/12 and 2/5 respectively.

a)If the production line A produced x bulbs,express the number of bulbs produced b y production line B in terms of x.

b)If the production line C produced 440 bulbs,find the number of bulbs produced by production line A.

Thx very much!!!!

2 個解答

評分
  • 6 年前
    最愛解答

    First, let a be the number of bulbs produced by production line A.

    Let b be the number of bulbs produced by production line B

    Let c be the number of bulbs produced by production line C

    (a)

    As the production line A produced x bulbs

    So, (x)/(x+b+c)=5/12...(1)

    For production line B, (b)/(x+b+c)=2/5...(2)

    From(1),

    (x)/(x+b+c)=5/12

    12x=5x+5b+5c

    -5b=-7x+5c...(3)

    From(2),

    (b)/(x+b+c)=2/5

    5b=2x+2b+2c

    3b=2x+2c...(4)

    (3)*2,

    -10b=-14x+10c...(5)

    (4)*5

    15b=10x+10c...(6)

    (5)-(6),

    -25b=-24x

    b=(24x)/25

    So, the number of bulbs produced by production line B is (24x)/25.

    (b)

    From(a), (1)

    (x)/(x+b+c)=5/12

    From(a), b=(24x)/25

    And from the question, c=440

    So,

    (x)/(x+((24x)/25)+440)=5/12

    12x=5x+(24/5)x+2200

    (11/5)x=2200

    11x=11000

    x=1000

    So, the number of bulbs produced by production line A is 1000 bulbs.

    資料來源: Me
  • 土扁
    Lv 7
    6 年前

    (a)

    Let n be the no. of bulbs produced by line B.

    (No. of bulbs produced by line A) : (No. of bulbs produced by line B)

    x : n = (5/12) : (2/5)

    (5/12)n = (2/5)x

    n = (2/5)(12/5)x

    n = 24x/25

    2015-01-04 21:32:53 補充:

    (b)

    Let m be the bulbs produced by line A.

    (No. of bulbs produced by line A) : (No. of bulbs produced by line C)

    m : 440 = (5/12) : [1 - (5/12) - (2/5)]

    m : 440 = (25/60) : (11/60)

    m : 440 = 25 : 11

    11m = 11000

    m = 1000

    No. of bulbs produced by line A = 1000

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