Question
There are is chest containing only diamond and emeralds
in the ratio 2:5. When 2 of them are picked at random form the chest, the probability that both are diamonds is 1/14. What is the difference between the number of diamonds and emeralds?Solution
Let the number of diamonds and emeralds in the chest be 2k and 5k respectively.
P(2 diamonds) = 1/14
( 2k C2 )/( 7k C2 ) = 1/14
2k(2k - 1)/7k(7k - 1) = 1/14
7k - 1 = 4(2k - 1)
7k - 1 = 8k - 4
k = 3
Required difference = 5k - 2k = 9
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