In tennis you win a game if you score four points before your opponent scores three points. Or, if you both score three points at some stage you win if you manage to score two points in a row after the three-all stage before your opponent does. Suppose that you have a fixed chance of 0.6 of winning any given point.
(i) How can a game be represented?
(ii) What is the shortest possible game?
(iii) How many different sorts of games result in two losses and four wins?
(iv) What is the probability of a game hitting deuce? (i.e. three points each)
(v) What is your chance of winning a game?
Source: Adapted from nrich.maths.org University of Cambridge
Reproduced by permission of NRICH Project, Centre for Mathematical Sciences, University of Cambridge