 Hello and welcome to the session. In this session we will discuss a question which says that the main diagram shows the number of people in a sports club who play tennis and here it is represented by capital letter T and number of people who play hockey which is represented by capital letter H. Now we have to determine the probability of the following events. First is people playing at least one of the two sports. Second is people playing tennis but not hockey. Now let us start with the solution of the given question. Now we know that probability of an event is equal to number of individual outcomes and different number of outcomes. Now in the given main diagram we have the number of people who play tennis and hockey. Now from this main diagram we see that number of people who play only tennis is equal to 15. That is this shaded portion represents number of people who play only tennis and this blue shaded portion represents number of people who play only hockey. So here number of people who play only hockey is equal to 26 and this pink shaded portion represents number of people who play both the games. So number of people who play both the games is equal to 27. Number of people who play none of the games is equal to 7 which lie outside the two circles. Now the total number of people in the club is equal to number of people who play only tennis plus number of people who play only hockey plus number of people who play both the games plus number of people who play none of the games. So this is equal to 15 plus 26 plus 27 plus 7 which is equal to 75. Now in the first part we have to find the probability of this event. Now let A be the event which is equal to people playing at least one of the games. It means it will include either hockey or tennis or both the games. So here number of people out comes is equal to number of people playing only tennis which is 15 plus number of people who play only hockey which is 26 plus number of people who play only hockey which is 26 plus number of people who play only hockey which is 25. Number of people who play both the games that is 27 and this is equal to 68. This means number of people playing at least one of the games is equal to 68 and total number of out comes that is total number of people in the club is equal to 75. So probability P of event A is equal to number of people playing at least one of the games upon total number of people in the club which is equal to 68 upon 75. Therefore probability P of event A is equal to 68 upon 75. Now in the second part we have to find the probability of this event. Now here we have to find probability of the people playing tennis but not hockey. Now here we know that number of people who play tennis only is equal to 15. Now we do not count 27 because these people play hockey as well and we need to find the people that is the number of people who play only tennis. So probability P of the people playing tennis but not hockey is equal to number of people who play only tennis upon total number of people in the club. And this is equal to 15 upon 75 which is equal to now 15 into 1 is 15 and 15 into 5 is 75 so this is equal to 1 upon 5. Therefore probability of the people playing tennis but not hockey is 1 upon 5. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.