can you explain in detailed steps

3. Questions on Sets, Counting, and Probability. (a) Suppose that A and B are events from a sample space S. Denote the probability of A and B as p(A) and p(B) respectively. (i) Let S = {S ($2. Sa. SA. Ss), A = {S]. S2. SA], and B = {$2.Ss). Assuming each sample s;, i = 1, ...,4 is equally likely but s, happens as twice likely as the rest of the samples. Determine the values of p(A) and p(B) respectively. Justify your answer. [5 marks] (ii) Under the same conditions given in (i), determine the conditional probability p(A|B). Justify your answer. [4 marks] (iii) Given that p(A) # 0 and p(B) # 0, show that if p(B|A)