 Hello and welcome to the session. In this session we discuss the following question which says, a community has two schools A and B, 60% of the community students are at A and 40% are at B. At school A, 70% of the students are science students and at school B, 40% of the students are science students. One student in the community is randomly chosen and is found to be a science student. What is the probability that the student attends school A? Before moving on to the solution, let's recall the base theorem. According to this we have that if E1, E2 and so on up to En are the events which constitute the partition of sample space that is their pairwise disjoint or you can say the sample space S is equal to E1 union, E2 union and so on, union En and A, B and E event with non-zero probability. Then we have the conditional probability of the event EI given that event A has already occurred is equal to probability of the event EI into probability of or the conditional probability of the event A given that event EI has already occurred upon submission J goes from 1 to N probability of EJ into conditional probability of the event A given that event EJ has already occurred. This is the key idea that we use for this question. Now we move on to the solution. We consider that E1 be the event that the student attends school A and we take that E2 be the event that the student attends school B and we take E be the event that the student is a science student. In the question we have that one student in the community is randomly chosen and is found to be a science student we have to find the probability that the student who is chosen is the student who attends school A. So we have to find the conditional probability of the event even given that event E has already occurred. Now probability of even that is probability of the event that the student attends school A is given by 6 upon 10 since it is given to us that 60% of the students are at school A so 60 upon 100 means 6 upon 10 so probability of even would be equal to 6 upon 10 next we find out the probability of E2 that is probability of the event that the student attends school B as in the question we have that the 40% of the students are at school B so 40 upon 100 that is 4 upon 10 is the probability of the event E2 next probability of or the conditional probability of the event E given that event even has already occurred is given as now as in the question we have that at school A 70% of the students are science students so it would be 7 upon 10 that is probability of or the conditional probability of the event E given that even already occurred is equal to 7 upon 10 then the conditional probability of the event E given that E2 has already occurred is given by 4 upon 10 since it is given to us that 40% of the students at school B are science students so this is equal to 4 upon 10 so the conditional probability of the event even given that event E has already occurred is equal to using the Bayes theorem this is equal to probability of even into conditional probability of the event E given that even has already occurred upon probability of event even into conditional probability of the event E given that event even has already occurred plus probability of event e2 into conditional probability of event e given that e2 has already occurred. So this would give us the probability that the student who is chosen from the community is a science student and here density school A. So this would be further equal to probability of even which is 6 upon 10 into probability of e given that even has occurred that is 7 upon 10 upon probability of even which is 6 upon 10 into 7 upon 10 plus 4 upon 10 into 4 upon 10. So this is equal to 42 upon 42 plus 16 which is equal to 42 upon 58 now 2 21 times is 42 and 2 29 times is 58 so this is equal to 21 upon 29 so we say the required probability is equal to the conditional probability of the event even given that e has already occurred is equal to 21 upon 29 so this is our final answer this completes the session hope you have understood the solution of this question