 Hello and welcome to the session. In this session we will discuss a question which says that a game is played by Ellie and Archie. In this game two dice are rolled. If a total of three or two comes then Ellie gets a point and if a total of eight or nine comes then Archie gets a point and if any other total comes on the two dice nobody receives a point. The player who gets first thirty points wins the game. Do you think one player have better chance of winning the game or both the players have equal chance explain using probability. Now before starting the solution of this question we should know a result and that is in a non uniform probability model all outcomes are not equally likely. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in this question a game is being played between Ellie and Archie with two dice and here it is given that Ellie gets a point when a total of three or two appears on the dice and Archie gets a point when a total of eight or nine appears on the dice. Now let us discuss the sample space of rolling two dice. Now we do that whenever we roll a die then total number of outcomes are six that is the number one two three four five and six. Now here we are rolling two dice simultaneously. So here we can get any of the numbers from one to six on the first dice and on the second dice. So here the first outcome that we can have is getting a number one on the first dice and getting, again a number one on the second dice and the second outcome that we can have is getting a number one on the first die and getting a getting a number 2 on the second row and the third outcome that we can have is getting a number 1 on the first row and getting a number 3 on the second row get all these outcomes when two guys are rolled simultaneously and here the total number of outcomes are 36. Now first of all let us find the number of favorable outcomes for any. Now any gets a point when a total of 3 or 2 appears on the dice. Now here these are the three outcomes in which total of the two numbers is either 3 or 2. Now here you can see that 1 plus 1 is 2, 1 plus 2 is 3 and 2 plus 1 is also 3. So for any number of favorable outcomes is equal to 3 that is these three outcomes. So the probability P of getting a total of 2 or 3 on the dice is equal to number of favorable outcomes which is 3 upon total number of outcomes which is 36 so this is equal to 0.083. Now let us find the number of favorable outcomes for Archie. Now we know that Archie gets a point when a total of 8 or 9 appears on the dice. Now from here you can see that these are the outcomes in which total of the two numbers is either 8 or 9. Now here you can see that 2 plus 6 is 8, 3 plus 6 is 9, 3 plus 5 is 8, 4 plus 5 is 9, 4 plus 4 is 8, 5 plus 4 is 9, 5 plus 3 is 8, 6 plus 2 is 8, 6 plus 3 is 9. So number of favorable outcomes for Archie is 1, 2, 3, 4, 5, 6, 7, 8 and 9. So probability P of getting a total of 8 or 9 on the dice is equal to number of favorable outcomes which is 9 upon total number of outcomes which is 36. So this is equal to 0.25. Now from here you can see that 0.25 is greater than 0.083. It means probability of getting a total of 8 or 9 is greater than probability of getting a total of 2 or 3. It means the chances of getting a total of 8 or 9 are greater than the chances of getting a total of 2 or 3. So both Annie and Archie do not have equal chance of winning. Also it is given in the question that the player who gets first 30 points wins the game and also we know that Archie gets a point when a total of 8 or 9 appears on the dice and Annie gets a point when a total of 3 or 2 comes on the dice. Now here as the chances of coming a total of 8 or 9 are greater so we will collect 30 points much earlier than Annie therefore Archie is more likely to win the game. And this is the solution of the given question. That's all for this session hope you all have enjoyed the session.