Suppose that two teams,
say the Braves and Indians, are playing a best of 5 series of
games.
Assume that the probability that the Braves win each game
is a fixed number p. A bookmaker remarks
that in his opinion the
probability that the Braves win the series in 3 games is the same
as the probability
that the Braves win the series in 5 games.
Assuming that the bookmaker is correct, find the exact value of p
(not a decimal approximation). A more difficult puzzle,
requiring the techniques of a basic probability course,
is the following. Suppose that in a best of 7 series
one bookmaker says the probability that the Braves will
win in 7
is the same as the probability that the Indians will win in 6.
Another bookmaker says the reverse.
That is, the probability
that the Braves will win in 6 is the same as the probability that
the Indians will win in 7.
Which bookie would you say favors the
Braves more? For each bookie find p, the probability that the
Braves
win each game, to justify your answer.