 Hello and welcome to the session. In this session, we will discuss a question which says that a high school talent, the number of males and females that with the members of the school club find each parability. First part is, a student is a member of the club given that he is a male. Second part is, a student is not a member of the club given that she is a female. And in third part, a student is a male given that he is not a member of the club. Now before starting the solution of this question, we should know our result. And that is, in two more tables, conditional probability of occurrence of event A given that event B occurs is equal to probability of event A intersection B upon probability of event B which is equal to frequency of event A intersection B upon frequency of event B. 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 here a two-way table is given to us and this table shows the number of students, males and females showing numbers and non-members of the club. Now in the first part we have to find the probability that a student selected is a member of the club given that he is a male. First of all let us define the events. Now let event A is student is a member of club and event B is student is a male. Now in the table we are given club and no-club in columns and male and female in rows. So in this table, club is event A, male is event B. Now we see that no-club will be event A bar or we can say event not A that is event A not happening. Also A bar denotes A complement similarly female will be event not male so it will be event B bar denotes B complement or we can say B bar denotes event B not happening. Now we have to find probability that a student selected is a member of the club. The student is a male it means here we have to find conditional probability of occurrence of event A given that event B occurs. Now using this result which is given to us in the key idea this is equal to frequency of event A intersection B upon frequency of event B. Now we know that event A is student is a member of club and event B is student is a male so event A intersection B will be male members of the club. Now here we can find frequency or number of students belonging to the event A intersection B from this table. Now here you can see male members of the club are 156 it means number of students belonging to the event A intersection B is 156 so frequency of event A intersection B is equal to 156. Now let us find frequency of event B. Now event B is student is a male so to find frequency of event B we have to find total number of male students it will be total of no one that is 156 plus 242 which is equal to 398 so frequency of event B is equal to 398. Now we have found frequency of event A intersection B and frequency of event B so this conditional probability will be equal to frequency of event A intersection B that is 156 upon frequency of event B that is 398. Now we know that 2 into 78 is 156 and 2 into 199 is 398 so this is equal to 78 upon 199 so the probability that a student selected is a member of the club given that student is a male is 78 upon 199. Now in the second part we have to find the probability that a student selected is not a member of the club given that she is a female. Now we know that event A complement is student is not a member of a club and event B complement is student is a female. So in the second part we have to find conditional probability of a grand supplement A complement given that event B complement occurs now this will be equal to probability of event B complement intersection B complement upon probability of event B complement now this will be equal to frequency of event A complement intersection B complement upon frequency of event B complement. Now event A complement intersection B complement will will be the female members who are not the members of the plot. Now from this 2-way table you can see frequency of event A complement intersection B complement is equal to 108. Now we want to find frequency of event B complement and that is total of row 2 that is 312 plus 108 which is equal to 420. So frequency of event B complement is equal to 420. Now putting these values here we have this conditional probability is equal to 108 upon 420. Now we do that 12 into 9 is 108 and 12 into 35 is 420. So this is equal to 9 upon 35. The probability that a student selected is not a member of the plot given that the student is a female is 9 upon 35. Now let us start with the third part where we want to find probability that a student selected is a member given that he is not a member of the plot. Now we know that event B is the student is a male and event B complement is student is not a member of the plot. This means here we have to find conditional probability of occurrence of event B given that event A complement occurs. Now this is equal to frequency of event B intersection A complement upon frequency of event A complement. Now here the event B intersection A complement will be the main members who are not members of the plot and here you can see this number is 232. So frequency of event B intersection A complement is equal to 232. Now we want to find frequency of event A complement. Now total of column 2 will give us frequency of event A complement and this is 232 plus 108 which is equal to 350. So frequency of event A complement is equal to 350. Now using these values conditional probability of occurrence of event B given that event A complement occurs is equal to 232 upon 350. Now 2 into 121 is 242 and 2 into 175 is 350. So this is equal to 121 upon 175. So the probability that a student selected is a male given that he is not a member of the club is 121 upon 175. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.