If you are rolling a balanced die twice what is the total co

If you are rolling a balanced die twice, what is the total count of the sample space S? If A

= { the two numbers add up to 7}, B = {one of them is odd and the other one is even} and

C = {the two numbers are different}, find P(A), P(B) and P(C). Then find P(A & B), P(A

& C) and P(B & C), where

total count of the sample space = 6 * 6 = 36

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

P(A) = 6/36 = 1/6

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

P(B) = 18/36 = 1/2

C = S- {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

P(C) = (36-6)/36 = 5/6

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

P(A&B) = 6/36 = 1/6

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

P(A &C) = 6/36 = 1/6

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

P(B & C) = 18/36 = 1/2

A and B are not independent

B and C are not independent

A and C are not independent

P(A/B) = P(A&B)/P(B) = 1/6/1/2 = 1/3

P(A/C) = P(A & C)/P(C) = 1/6/5/6 = 1/5

P(B/C) = P(B & C)/P(C) = 1/2/5/6 = 3/5