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by yellowho » Wed Jan 19, 2011 11:36 pm
Set X = [1,4,3,6,9,12,15]. If three different numbers are randomly selected from Set A, what is the
probability that the sum of the numbers is not divisible by 3?
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by Rahul@gurome » Thu Jan 20, 2011 1:17 am
yellowho wrote:Set X = [1,4,3,6,9,12,15]. If three different numbers are randomly selected from Set A, what is the
probability that the sum of the numbers is not divisible by 3?
Note that out of 7 integers 5 are divisible by 3. Hence when any three of them are selected, the sum will be divisible by 3. Apart from those triplets no other triplet is possible such that the sum will be divisible by 3.

Hence, number of possible triplets such that the sum is divisible by 3 = Number of possible different selections of 3 integers out of 5 = 5C3 = 10

Total number of possible different selections of 3 integers out of 7 = 7C3 = 35

Hence, required probability = 1 - (10/35) = 25/35 = 5/7
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