Need help with a discrete mathematics problem, please show all work. It will help me check my work, and explain concepts to me, thank you

2. (20 points) Two events E1 and E2 are called independent if p(ElE2) = p(E1)p(E2). For the following pairs of events, nd the values of p(E1), p(E2), and p(E1 0E2) when a coin is tossed three times. Then determine whether or not they're independent. (a) El: tails comes up when the coin is tossed the rst time, E2 heads comes up when the coin is tossed the second time (b) E1: tails comes up when the coin is tossed the rst time, E2: exactly two heads come up in a row (0) E1: tails comes up when the coin is tossed the second time, E2: exactly two heads come up in a row ((1) Assume that E1 and E2 are independent events, prove that their complements are also independent events