A computer game stimulate a match beteewn A and B. The match consist of at most 3 sets. Each set is won by either A or B and the match is won by 1st player to win the two sets.
The stimulation uses the following rules:
-The probability that A wins the 1st set is 0.6
-For each set after the 1st, the conditional probability that A wins that set, given that A won the preceding set, is 0.7
-For each set after the 1st, the cnditional probability that B wins that set, given B won the preceding set, is 0.8
Find the probability that (i)A wins the second set
(ii)A wins the match