Consider independently rolling two fair dice, one red and the other green. Let ?A be the event that the red die shows 3 dots, ?B ?be the event that the green die shows 4 dots, and ?C ?be the event that the total number of dots showing on the two dice is 7. Are these events pairwise independent (i.e., are ?A ?and ?B ?independent events, are A ?and ?C ?independent, and are ?B ?and ?C ?independent)? Are the three events mutually independent?

Answer Step 1 of 6 The probability of each of these events is 1/6. P(A)=, P(B)=, P(c)=1/6 If P(A B) = P(A)*P(B), then the events A and B are independent. Step 2 of 6 A and B are plainly independent events. P(A & B) = 1/36 = (1/6) (1/6) = P(A) P(B) Step 3 of 6 Finding P(A C). the possible outcomes of C are {C} = {(R=3,G=4), (R=4,G=3), (R=2,G=5), (R=5,G=2), (R=1,G=6), (R=6,G=1)}. event A is defined as R=3 in the set of possible outcomes for C {A C} = {(R=3,G=4)}. Now P(A C) = P(R=3)*P(G=4) = P(A)*P(B) = (1/6)*(1/6) = 1/36.