# 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

• 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
• (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