Question 665417
Two dice are rolled

( 1 , 1 ), ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
( 2 , 1 ) ( 2 , 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 2 , 5 ) ( 2 , 6 )
( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 ) ( 3 , 4 ) ( 3 , 5 ) ( 3 , 6 )
( 4 , 1 ) ( 4 , 2 ) ( 4 , 3 ) ( 4 , 4 ) ( 4 , 5 ) ( 4 , 6 )
( 5 , 1 ) ( 5 , 2 ) ( 5 , 3 ) ( 5 , 4 ) ( 5 , 5 ) ( 5 , 6 )
( 6 , 1 ) ( 6 , 2 ) ( 6 , 3 ) ( 6 , 4 ) ( 6 , 5 ) ( 6 , 6 )

n(S)=36

Let A be the event that the sum on the top face be even

A={( 1 , 1 ),  ( 1 , 3 )  ( 1 , 5 )  ( 2 , 2 )  ( 2 , 4 ) ( 2 , 6 )( 3 , 1 ) ( 3 , 3 )  ( 3 , 5 )  ( 4 , 2 )  ( 4 , 4 ) ( 4 , 6 )( 5 , 1 )  ( 5 , 3 )  ( 5 , 5 )  ( 6 , 2 )  ( 6 , 4 )  ( 6 , 6 )}

n(A)= 18

p(A)= 18/36= 1/2

B is the eventy that the sum on upper face is 6 or less than 6

B={( 1 , 1 ), ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
( 2 , 1 ) ( 2 , 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 ) 
( 4 , 1 ) ( 4 , 2 ) ( 5 , 1 ) }

n(B)=16
p(B)= 16/36 = 4/9


(A n B) =( 1 , 1 ),  ( 1 , 3 )( 1 , 5 )( 2 , 2 ) ( 2 , 4 )( 3 , 1 )( 3 , 3 )( 4 , 2 ) ( 5 , 1 )}
n(AnB)= 9
p(AnB)= 9/36 = 1/4 

p(A u B) = p(A)+p(B) -p(a n B)
= 1/2 +4/9 -1/4
=(18+16-9)/36
=23/36

 P(AIB) = .6
or, P(A and B)/P(B) = 0.6
or, P(A)*P(B)/P(B) = 0.6
or, P(A) = 0.6

So, A and B are independent.