Roll two dice Let Athe sum is even and Bthe sum is divisible

Roll two dice. Let A=\"the sum is even\" and B=\"the sum is divisible by 3\", that is, B={3,6,9,12}. Are A and B independent?

Solution

a contains events=(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)= 18 P(A)=1/2 SIMILARLY FIND P(B) {=1/3} AND P(A INTERSECTION B) {= 1/6} FIND P(A/B)= P(A INTERSECTION B)/P(B) WILL COME OUT TO BE EQUAL TO P(A) SO TWO EVENTS ARE INDEPENDENT