IIT JEE , AIEEE Forum - Mathematics , Algebra

akhil_o

(x-y)(x+y) must be divisible by 3
so (x-y) or (x+y) or both (x-y)(x+y) are divisible by 3

for x-y divisible by 3
m=3k+1,n=3k+1 or m=3k+2,n=3k+2 or m=3k,n=3k

P(A)=1/3*1/3+1/3*1/3+1/3*1/3=1/3

for x+y divisible by 3
m=3k+1,n=3k+2 or m=3k+2, n=3k+1, m=3k and n=3k
=1/3*1/3+1/3*1/3+1/3*1/3=1/3

for both divisible by 3
1/3*1/3=1/9

P(A)UP(B)=P(A)+P(B)-p(A intersection B)
=1/3+1/3-1/9
=5/9

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