Consider the experiment of tossing a fair coin three times. A sample point for this experiment must indicate the result of each toss. For example, HHT could indicate that two heads, then a tail were observed. Let Hi, where i=1,2,3, denote the event that the ith toss is head. For example, H1={HHH, HHT, HTH, HTT}.
Answer to the following questions with your explanation:
(a) Compute P(H1), P(H2), and P(H3).
(b) Compute P(H1∩H2) and P(H1∩H2∩H3).
(c) Are the events H1, H2, and H3 mutually independent?