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

#1**+1 **

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