4. Let X be the set of binary strings of length 4. Thus, X1 = 24 = 16. 6) Let A be set of strings a X which contain 00 as a substring. Use inclusion-exclusion to determine A). Hint: For 1 {1,2,3), let Abe the set of strings a e X that contain a 00 beginning at position i. For example, 0010 A, 1001 A2, and 0100 Ag. [No marks without using inclusion-exclusion.] [4] (ii) Let B be the set of strings be X which contain 11 as a substring. What is | B|? (1) Let A and B be defined as above. Suppose we select a string * e X uniformly at random. Let a be the event that a A and B be the event that I e B. Are a and 8 independent events? [3]