In each of the following cases, find the probability that a binary string of length 8 begins with 10 or contains exactly four 0-s if the bits are independent.
(i) 0 and 1 are equally likely to appear in any place;
(ii) the probability that a bit is 1 is 0.6;
(iii) the probability that bit i is 0 is 1/2i for i = 1,2,...8.
