7. A computer game simulates a tennis match between two players,
A and B. The match consists of at most three sets. Each set is won
by either A or B, and the match is won by the first player to win
two sets.
The simulation uses the following rules.
- The probability that A wins the first set is 0.6.
- For each set after the first, the conditional probability that
A wins that set, given that A won the preceding set, is 0.7.
- For each set after the first, the conditional probability that
B wins that set, given that B won the preceding set, is 0.8.
Calculate the probability that
(i) A wins the second set, [2]
(ii) A wins the match, [3]
(iii) B won the first set, given that A wins the match. [3]
