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# help in maths

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safia puts some brown counters and some purple counters into an empty box. The ratio of the number of brown counters to the number of purple counters is 1:4. Hanadi takes at random 2 counters from the box. The probability that she takes 2 brown counters is 17/445. How many counters of each colour did safia put inro the box?

ludo123  Mar 26, 2018
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Let the number of brown counters  = B....so....the number of purple counters is 4B

So....the total number of counters is 5B

So.....

The probability of taking a brown one on the 1st draw is   B / [B + 4B]  = B / 5B  = 1/5

The probability that a brown one is taken on the second draw is  [ B -1]  / [ 5B - 1]

So....the total probability is

[1/5 ]  * [ B - 1 ] / [ 5B - 1]  = 17/ 445

[ B- 1] / [ 5B - 1]  = 17/89   cross multiply

89 [ B - 1 ]  =  17 [ 5B - 1]

89B - 89  = 85B - 17       add/subtract  89, 85B to/from  both sides

4B = 72     divide both sides by 4

B = 18  =  the original number of brown  counters

4B  = 72  =   the original number of purple counters

CPhill  Mar 26, 2018

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