Separate dependent sets from independent repeated matches

A and B play a racquet match of at most 3 sets. The first to win two sets wins. A wins the first set with probability 0.6. After the first set, A wins the next set with probability p given A won the preceding set; B wins the next set with probability 0.7 given B won the preceding set.

Find, in terms of p, the probability that A wins the match.

(i) The probability B won the first set given B lost the match is 0.15. Find p.2 marks

(ii) Given instead p=0.65 and that A’s third win occurs in the nth match with probability 0.10866 correct to 5 significant figures, write an equation for n and solve it numerically.3 marks