A fair coin is tossed five times in succession. Define the following events:
A = "the first toss results in a head",
B = "the last toss results in a tail".
a. (i) Verify, by direct computation, that events A and B are independent.
b. (ii) Using your result from part (i), find the probability that both A and B occur in a single sequence of five tosses.
c. (iii) Suppose the entire experiment of five tosses is repeated independently 100 times. Find the expected number of sequences in which both A and B occur together.