Exercise 3.5. Two dice are simultaneously rolled. For each pair of events defined below, compute if they are independent or not.

(a) A1 = {the sum is 7}, B1 = {the first die lands a 3}.

(b) A2 = {the sum is 9}, B2 = {the second die lands a 3}.

(c) A3 = {the sum is 9}, B3 = {the first die lands even}.

(d) A4 = {the sum is 9}, B4 = {the first die is less than the second}.

(e) A5 = {two dice are equal}, B5 = {the sum is 8}.

(f) A6 = {two dice are equal}, B6 = {the first die lands even}.

(g) A7 = {two dice are not equal}, B7 = {the first die is less than the second}.

Exercise 3.6. Are the events A1, B1 and B3 from Exercise 3.5 jointly independent?

No need to solve exercise 3.5, just do 3.6, thank you!