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  3. 3.17 you and i play a tennis match. it is deuce, w

3.17 You and I play a tennis match. It is deuce, which means if you win...

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Statistics

3.17 You and I play a tennis match. It is deuce, which means ifyou win the
next two rallies, you win the game; if I win both rallies, I winthe game; if
we each win one rally, it is deuce again. Suppose the outcome of arally is
independent of other rallies, and you win a rally with probabilityp. Let W be
the event “you win the game,” G “the game ends after the next tworallies,”
and D “it becomes deuce again.”
a. Determine P(W | G).
b. Show that P(W) = p2 + 2p(1 − p)P(W | D) and use P(W) = P(W |D)
(why is this so?) to determine P(W).
c. Explain why the answers are the same.

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