 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says Bag 1 contains 3 red and 4 black balls and bag 2 contains 4 red and 5 black balls One ball is transferred from bag 1 to bag 2 and then a ball is drawn from bag 2 The ball so drawn is found to be red in color. Find the probability that the transferred ball is black Now we know that according to the Bayes theorem Even e2 so on e n are events which constitute a Partition of sample space s that is even e2 so on till e n are pairwise disjoint and Even union e2 union so on union e n is equal to s and a be 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 J varying from 1 to n So this is a 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 According to the question bag 1 contains 3 red and 4 black balls and back to contains 4 red and 5 black balls Now one ball is transferred from back 1 to back 2 and then a ball is drawn from back 2 so let Even be the event that The ball transferred From bag 1 is red to be the event that the ball transferred from bag 1 is Black therefore probability of e 1 is equal to 3 upon 7 and Probability of e 2 is equal to 4 upon 7 Again according to the question when a ball is drawn from back to the ball is found to be red in color let a be the event of Drawing a red ball Back to contains 4 red and 5 black balls After transferring a red ball from back 1 to back 2 the back 2 will have 5 red and 5 black balls Now probability of drawing a red ball given The transferred ball is red That is Probability of a upon even now this is equal to 5 upon 10 Which is equal to 1 over 2 now? probability of drawing a red ball given That the transferred ball is Black that is probability of a upon e2 Now again, we know that back to contains 4 red and 5 black balls So when a black ball is transferred from back 1 to back 2 it will have 4 red and 6 black balls So probability of a upon e2 is equal to 4 upon 10 which is equal to 2 over 5 Now we have to find the probability that the transferred ball is black So the probability That the transferred ball is black being given that The ball drawn is red So this is given by probability of e2 upon a So by using Bayes theorem we have probability of e2 upon a is equal to probability of e2 into probability of a upon e2 over probability of even into probability of a upon e1 plus probability of e2 into probability of a upon e2 Now we have probability of even is 3 upon 7 probability of e2 is 4 upon 7 and probability of a upon e1 is 1 over 2 and probability of a upon e2 is 2 over 5 So this is equal to 4 over 7 into 2 over 5 over 3 over 7 into 1 over 2 plus 4 over 7 into 2 over 5 and this is equal to 8 over 35 over 3 over 14 plus 8 over 35 and this is equal to 8 over 35 over 15 plus 16 over 70 and this is again equal to 8 over 35 into 70 over 31 this is again equal to 16 over 31 Hence the probability that the transferred ball is black is 16 over 31 So this is the answer for the above question This completes our session. I hope the solution is clear to you. Bye and have a nice day