Predict future weather using the probability that tomorrow is wet
given today is wet and the probability that tomorrow is wet given
that today is dry.
If the score is 8-8 do I have more chance of winning if the winner
is the first to reach 9 points or the first to reach 10 points?
It is believed that weaker snooker players have a better chance of
winning matches over eleven frames (i.e. first to win 6 frames)
than they do over fifteen frames. Is this true?
In a particular snooker tournament, two players play "frames"
against each other and the first to win 8 frames wins the match.
This is known as a "best of 15" match. Assume that the probability
of player A winning each frame is $p$, regardless of who starts. If
A does not win the frame then his opponent does (there are no
Suppose $p = 0.4$, then what is the probability that A wins the
match? Now suppose that A is very slightly better than his
opponent, say $p = 0.55$, what is the probability now of A winning
the match? What is the probability of A winning the match when $p =