 Hi and welcome to the session I am Deepika and I am going to help you to solve the following question. The question says there are two bags one and two that one contains two white and three red balls and back two contains four white and five red balls one ball is drawn at random from one of the bags and is found to be read. Find the probability that it was drawn from back two. So let's start the solution. According to the given question there are two bags one and two and back one contains two white and three red balls and back two contains four white and five red balls. One ball is drawn at random from one of the bags and is found to be read. So let even be the event of choosing the bag one it to be the event of choosing the bag two let A be the event choosing a red ball then probability of E1 is equal to probability of E2 is equal to 1 over 2 also probability of A upon E1 that is probability of drawing a red ball from bag one is equal to 3 over 5 because bag one contains two white and three red balls so probability of drawing a red ball from bag one is 3 over 5. Now bag two contains four white and five red balls so probability of A upon E2 that is probability of drawing a red ball from bag two is equal to five upon nine. Now again according to the question one ball is drawn at random from one of the bags and is found to be read we have to find the probability that it was drawn from back two. Now the probability of drawing a ball from bag two being given that it is read is probability of E2 upon A so by using base theorem we get probability of E2 upon A is equal to probability of E2 into probability of A upon E2 over probability of E1 into probability of A upon E1 plus probability of E2 into probability of A upon E2. Now we have probability of E1 is equal to probability of E2 is equal to 1 over 2 and probability of A upon E1 is equal to 3 over 5 and probability of A upon E2 is equal to 5 over 9 so on substituting these values we have probability of E2 upon A is equal to 1 over 2 into 5 over 9 over 1 over 2 into 3 over 5 plus 1 over 2 into 5 over 9 and this is again equal to 5 over 18 upon 3 over 10 plus 5 over 18 and this is again equal to 5 over 18 upon 27 plus 25 over 90 and this is equal to 5 over 18 into 90 over 52 and this is again equal to 25 over 52 so probability of E2 upon A is 25 over 52 that is the probability of drawing a ball from bag two being given that it is read is 25 over 52 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