Tennis is a universal sport. Just like any other sport, tennis has its own unique terminology and scoring system. During a game broadcast on TV, viewers are usually given the opportunity to see a variable number of statistics. These statistics would include the number of aces, first and second serve percentages, number of winners and errors, and so on. The average viewer would only know who won, but these statistics provide much more in-depth information about many underlying aspects of the match, such as how a player won and their chances of winning. Meanwhile, the construction of probability formulas is present since the scoring system is hierarchically structured. For example, points are earned during service games; these points are nested within sets, as well as within the match. Therefore, tennis is a mathematical game heavily involved in the chances of players winning the match2. Scoring a Tennis Match Tennis has a distinctive scoring system that can be confusing for many beginners or people who are simply unfamiliar with the sport. However, the basic scoring system involves having points needed to win matches, games needed to win sets, and sets needed to win the match.2.1 GamesThe score for a match typically starts at 0 (love), so man as the points are earned they will increase incrementally and become 15, 30, 40 respectively and then game. If both players reach 40 it is called a “deuce”. Likewise, whoever wins the next point gets the "advantage". If the leading player wins the next point, it's game on; however, if they lose the next point, they are back in a tie. Throughout the entire game, the batsman remains constant and will alternate between games. (Figure 2.1.1) This figure is him... in the center of the paper....... Therefore, the probability that the batsman wins the game without reaching par occurs with probability p^4+ 4p^4 q + 10p^4 q^2= p^4 (1 + 4q + 10q^2 ). The probability of the score reaching a tie occurs with probability 20 p^3 q^3 (since there are 20 paths that can occur to reach a tie and each player wins exactly 3 points). The probability of the server winning the game from deuce: To win the game from deuce the server must win the next two points. This occurs with probabilityp^2. If the server wins the next point by two followed by the receiver winning one point, or the receiver wins the next point by two followed by the server winning one point, the score returns to two. This happens with probability 2pq. If d is the probability that the batter wins the game when the score is tied, then d = p^2+ 2pqd. Solving d gives d=p^2/(1-2pq)