We select at random an integer from the sample space = {1, 2,, 20}. Consider the following

We select at random an integer from the sample spaceΩ = {1, 2,…, 20}. Consider the following three events in that sample space:

A = {4, 5,…, 13}, B = {9, 10,…, 18}, and C = {4, 5, 6, 7, 8} ∪ {14, 15,…, 18}.

(i) Show that the event A is independent from each of the events B and C.

(ii) Prove that the events A and BC are not independent.

(iii) Prove that the events A and B ∪ C are dependent.