Dear Team , Please check the question 5 of IAI of May 2012, where the login behind the win and loss formation is not clear . please check. question 5 Consider a game of tennis between two players Novak Djokovic and Andy Murray. A game of tennis begins with the score being 0-0. If a player wins a point, his score would move from 0 to 15 and likewise from 15 to 30 and 30 to 40 upon winning subsequent points. If a player, who is already on 40, wins the next point, he wins the game except if the other player is on 40 at that time or is holding an ―Advantage‖ at that time. If both players are on 40 each, such situation is termed as ―Deuce‖. The player winning the first point from the state of Deuce is said to hold an ―Advantage‖. If the player holding the advantage wins the next point, he wins the game. However, if the next point is instead won by the other player, the game reverts to Deuce. In a game, therefore, there are essentially 17 different states: 0-0, 15-0, 30-0, 40-0, 15-15, 30-15, 40-15, 0-15, 0-30, 0-40, 15-30, 15-40, Deuce, Advantage Djokovic, Advantage Murray, Game Djokovic, Game Murray. You may note that from a modeling perspective: 30-30 is identical to Deuce 40-30 is identical to Advantage Djokovic 30-40 is identical to Advantage Murray Let us assume that the probability of Djokovic winning a point is p, and that this probability is constant throughout the duration of the game. The probability of Murray winning a point may be denoted by q, where q = 1 – p. Let (,) denote the probability that Djokovic wins the game given that his score is i and Murray’s score is j. Calculate the probability (30,30) - the probability that Djokovic wins the game from a position where both players are on 30 each. Solution : The possible scenarios starting from 30-30 are as follows: WW WLWW, LWWW WLLWWW, LWLWWW, LWWLWW, WLWLWW how the examiner formulated this winning loss is not clear , please provide the logic.
This question looks like you need a bit of knowledge of the scoring in tennis, which isn't great for a CT4 exam, we shouldn't be examined on our tennis knowledge - if you have the energy... https://en.wikipedia.org/wiki/Tennis_scoring_system 30:30 means that to win the game, one player has to win 2 points before the other wins 1. Djokovic needs to win 2 more points before Murray wins 1 point. This could happen in the next 2 points... WW or in the next 4 points.. WLWW or LWWW or the next 6 points... WLWLWW or WLLWWW or LWWLWW or LWLWWW and so on... Notice that WL or LW both place us back where we started. Have a look at CT4 September 2007 Question 9 This question is extremely similar and, from the looks of it, much better worded because the match goes straight to Deuce and avoids the prerequisite tennis knowledge. Good luck! John
Further to this, please check out this forum post, where I explain where the probability comes from in Sep 2007 Q9... https://www.acted.co.uk/forums/index.php?threads/sep-2007-question-9-please-explain.11921/
