 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says Suppose we have four boxes A, B, C and G containing coloured marbles as given below. Box A contains one red, six white and three black marbles. Box B contains six red, two white and two black marbles. Box C contains eight red, one white and one black marble. Box G contains zero red, six white and four black marbles. One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A, box B, box C? Now we know that by Bayes theorem if even E2 so on, E n are evens which constitute a partition of sample space S. That is even E2 so on, E n are fair by disjoint and even union E2 union so on, union E n is equal to S. And A, B, any event with non-zero probability then probability of E i upon A is equal to probability of E i into probability of A upon E i over sigma probability of E j into probability of A upon E j where j varying from 1 to n. So this is the key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. Now according to the given question we have four boxes A, B, C and G. One of the boxes has been selected at random and a single marble is drawn from it. And the color of that single marble is red. Select A, even E2, E3, E4. Be the evens as defined below. A is the event a red marble is selected. Even is the event, box A is selected. Two is the event, box B is selected. E is the event, box C is selected. Four is the event, box D is selected. The boxes are chosen at random. Therefore probability of E1 is equal to probability of E2 is equal to probability of E3 which is equal to probability of E4. And this is equal to 1 over 4. Now box A contains one red marble. Box B contains six red marbles. Box C contains eight red marbles. And box D contains zero red marbles. That is it doesn't contain any red color marble. So probability of A upon E1 is equal to 1 over 10. Probability of A upon E2 is equal to 6 upon 10. And probability of A upon E3 is equal to 8 upon 10. And probability of A upon E4 is equal to zero upon 10 which is zero. Now we have to find the probability that the marble drawn was from box A. So the probability that box A is selected given that the drawn marble is red is given by probability of E1 upon A. Hence by Bayes theorem we have probability of E1 upon A is equal to probability of E1 into probability of A upon E1 over probability of E1 into probability of A upon E1 plus probability of E2 into probability of A upon E2 plus probability of E3 into probability of A upon E3 plus probability of E4 into probability of A upon E4 now we have probability of E1 is equal to probability of E2 which is equal to probability of E3 and this is again equal to probability of E4 which is equal to 1 over 4 probability of A upon E1 is 1 over 10 probability of A upon E2 is 6 over 10 probability of A upon E3 is 8 over 10 and probability of A upon E4 is equal to 0 so on substituting these values we have probability of even upon A is equal to 1 over 4 into 1 over 10 over 1 over 4 into 1 over 10 plus 1 over 4 into 6 over 10 plus 1 over 4 into 8 over 10 plus 1 over 4 into 0 and this is equal to 1 over 40 upon 1 plus 6 plus 8 over 40 and this is again equal to 1 over 40 into 40 over 15 and this is equal to 1 over 15 so the probability of even upon A is 1 over 15 that is the probability that box A is selected given that the drawn marble is read again we have to find the probability that the marble was drawn from box B so again by using Bayes theorem we have probability of E2 upon A is equal to probability of E2 into probability of A upon E2 over sigma probability of Ej into probability of A upon Ej j varying from 1 to 4 and this is equal to 1 over 4 into 6 over 10 over 1 plus 6 plus 8 over 40 this is equal to 6 over 40 into 40 over 15 and this is again equal to hence the probability that box B selected given that the drawn marble is read is equal to 2 over 5 similarly again we have to find the probability that the red marble was drawn from box C so by Bayes theorem we have probability of E3 upon A is equal to probability of E3 into probability of A upon E3 over sigma probability of Ej into probability of A upon Ej j varying from 1 to 4 and this is equal to 1 over 4 into 8 over 10 over 15 over 40 and this is again equal to 8 over 40 into 40 over 15 and this is again equal to 8 over 15 hence the probability that box C selected given that the drawn marble is read is 8 over 15 so the answer for the above question is 1 over 15 2 over 5 and 8 over 15 so this completes our session I hope the solution is clear to you bye and have a nice day