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Two distinct numbers x & y are chosen at random from the set {1,2,3,....,30}. The probability that x 2 -y 2 is divisible by 3 is: (A) ½ (B) ¼ (C) 2/3 (D) None of these

Two distinct numbers x & y are chosen at random from the set {1,2,3,....,30}. The probability that x2-y2 is divisible by 3 is:
(A) ½             (B) ¼ 
(C) 2/3           (D) None of these 
 
 

Grade:12

1 Answers

soumodip pal
26 Points
3 years ago
Total no. of cases is 30*29= 870
For favourable cases, either both x & y should divisible by 3 or none of them should divisible by 3. In the second scenario, the remainder can be 1 or 2 if x and y have same remainder x-y would be divisible by 3 if x & y have different remainder then x+y would be divisible by 8 .
such cases are (10*9) +(20*19) = 470
probability will be 47/87

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