There are some red counters and some white counters in a bag. At the start, 7 of the counters are red, the rest of the countries are white. Alfie takes at random a counter from the bag. He does not put the counter back in the bag. Alfie then takes at random another counter from the bag. The probability that the first counter Alfie takes is white and the second counter Alfie takes is 21 out of 80
Answers
Given : 7 of the counters are red the rest of the countries are white
Alfie takes at random a counter from the bag. He does not put the counter back in the bag
probability that 1st counter is white and second is red = 21/80
To Find : Number of White counters
Solution:
Red counter = 7
White counter = W
Total Counters = 7 + W
probability that the first counter Alfie takes is white and the second counter Alfie takes is 21/ 80
= ( W/(7 + W)) (7 /(7 + W - 1)) = 21/80
= ( W/(7 + W)) (1/(6 + W )) =3/80
=> 80W = 3(7 + W)(6 + W )
=> 80W = 3( W² + 13W + 42)
= 3W² + 39W + 126 = 80W
=> 3W² - 41W + 126 = 0
=> 3W² - 27W - 14W + 126 = 0
=> 3W(W - 9) - 14(W - 9) = 0
=> (3W - 14)(W - 9) = 0
=> W = 9 , W = 14/3 (should be integer)
Hence 9 White balls
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