(HELP PLEASE) For a single roll of two dice, are rolling a sum of 6 and rolling doubles independent events? Explain. 

If two events are independent, the occurrence of one event does not affect the other. That is if two events are independent, then P(Aâ©B)=P(A)P(B) Let A be the even getting a sum of 6 in a single roll of two dice. Sample space of A ={(1,5)(5,1)(2,4)(4,2)(3,3)} n(A)=5; n(S)=36 Therefore P(A) =n(A)/n(S) =5/36 ---------(1) Let B be the event of rolling doubles. Sample space for B ={(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)} n(B)=6;n(S)=36 P(B) = n(B)/n(S) = 6/36 --------------(2) Aâ©B is the event of getting a sum of 6 and rolling doubles. Therefore n(Aâ©B)=1 P(Aâ©B)=1/36 ------(3) Multiplying equation (1) and (2) (5/36)*(6/36)=5/216 but P(Aâ©B)=1/36 P(Aâ©B) ≠P(A)P(B) Therefore, the events are not independent.