7. In a men's singles tennis tournament, Andre and John are playing a match for the championship....
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7. In a men's singles tennis tournament, Andre and John are playing a match for the championship.
The match is won when either player wins three out of five sets. Statistics show that there is 60% chance that Andre will win anyone set.
(a) Express the match as a Markov chain.
(b) On the average, how long will the match last and what is the probability that Andre will win the championship?
(c) If the score is 1 set to 2, John's favor, what is the probability that Andre will win?
(d) In Part (c), determine the average number of sets till the match ends and interpret the result.
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