 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says If probability of A is equal to 6 upon 11 probability of B is equal to 5 upon 11 and probability of A union B is equal to 7 upon 11 finds probability of A intersection B probability of A upon B and probability of B upon A Now we know that the conditional probability of the event E given that F has occurred that is probability of E upon F is equal to probability of E intersection F upon probability of F provided probability of F is not equal to 0 So this is a key idea behind that question We will take the help of this key idea to solve the above question So let's start the solution Now in part one we have to find the probability of A intersection B. We are given probability of A is equal to 6 upon 11 probability of B is equal to 5 upon 11 and probability of A union B Is equal to 7 upon 11 Now we know that probability of A union B Is equal to probability of A plus probability of B minus probability of A intersection B So this implies probability of A intersection B is equal to probability of A plus probability of B minus probability of A union B and this is equal to now probability of A is equal to 6 upon 11 plus probability of B which is 5 upon 11 minus probability of A union B which is 7 upon 11 and this is equal to 11 minus 7 upon 11 and this is equal to 4 upon 11. So probability of A intersection B is equal to 4 upon 11. Now in part 2 we have to find the probability of A upon B. Now we are given probability of B is equal to 5 upon 11 and probability of A intersection B this is equal to 4 upon 11. So according to our key idea probability of A upon B is equal to probability of A intersection B upon probability of B and this is equal to 4 upon 11 into 11 upon 5 and this is equal to 4 upon 5. So probability of A upon B is equal to 4 upon 5. Now in part 3 we have to find the probability of B upon A. Now we are given probability of A is equal to 6 upon 11 and probability of A intersection B which is equal to probability of B intersection A and this is equal to 4 upon 11. Now according to our key idea we have probability of B upon A is equal to probability of B intersection A upon probability of A. Now probability of B intersection A is 4 over 11 and probability of A is equal to 6 upon 11. So probability of B upon A is equal to 4 upon 11 into 11 upon 6 and this is equal to 2 upon 3. So probability of B upon A is equal to 2 upon 3. Hence the answer for part 1 is 4 over 11 for part 2, 4 over 5 and the answer for part 3 is 2 upon 3. So this completes our session. I hope the solution is clear to you. Okay bye and take care.