 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that 15 musicians are surveyed to find out whether they play the violin or the piano. 7 play the violin, 9 play the piano and 3 play both the instruments. Find the probability that the musician plays piano given that he plays violin. We know that if A and B are two events then probability of occurrence of event A given event B is equal to probability of event A intersection B upon probability of event B where probability of event B is greater than 0. With this key idea we shall proceed to the solution. We are given that total number of musicians is 15, number of musicians playing violin is given as 7, number of musicians playing piano is given as 9 and number of musicians playing both violin and piano is given as 3. We have to find if a person is selected then what is the probability that he plays piano given he plays violin. Let event A be person plays violin and event B be person plays piano. We have to find the probability that a person plays piano given he plays violin that is probability of occurrence of event B given event A from the key idea we know that if A and B are two events then probability of occurrence of event A given event B is equal to probability of event A intersection B upon probability of event B where probability of event B is greater than 0. So here probability of occurrence of event B given event A will be equal to probability of event A intersection B upon probability of event A where probability of event A is greater than 0. Let us find favourable outcomes for event A intersection B and event A. Now event A intersection B is playing both violin and piano so number of people playing both instruments is equal to 3 similarly for event A that is person plays violin number of people playing violin is given to us as 7 and we know that total number of musicians given to us is 15. So probability of event A intersection B will be equal to favourable outcomes that is number of favourable outcomes which is equal to 3 upon total number of outcomes that is given to us as total number of musicians which is 15 so probability of event A intersection B will be 3 upon 15 and probability of event A which is equal to number of favourable outcomes upon total number of outcomes so number of favourable outcomes of event A is 7 upon total number of outcomes that is 15 so probability of event A is 7 by 15 so probability of occurrence of event B given event A is equal to probability of event A intersection B which is equal to 3 upon 15 whole upon probability of event A that is equal to 7 upon 15 and this is equal to 3 upon 7 So probability of occurrence of event B given event A is equal to 3 upon 7 that is the probability that a musician plays piano given that he plays violin is given as 3 upon 7 which is the required answer This completes our session. Hope you enjoyed this session.