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?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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?
(i) write down p(tomorrow is dry | today is wet)
and p(tomorrow is dry | today is dry)
On 1st June, when you are planning a picnic, the
weather will be either wet or dry. Let p(June 1st is wet) = p and
consequently p(June 1st is dry) = 1 - p
(ii) Write down p(June 2nd is wet) in terms of p.
Let p n denote the probability that the weather on
day n is wet given that the weather the day before is wet. Now
simplify the problem by making the assumption that the weather on
any given day depends only on the weather the day before and not on
the weather before then.
Use an iterative technique (with your calculator if you wish) to
(iii) p(July 1 st is wet | June 1 st is
(iv) p(July 1 st is wet | June 1 st is
(v) What do the answers to (iii) and (iv) tell you about
long-term future weather?