 Hello, I am welcome to the session, I am Deepika here. Let's discuss the question we see. If probability of A is equal to 0.8, probability of V is equal to 0.5 and probability of V upon A is 0.4, fine. Probability of A intersection V, probability of A upon B and probability of A union V. Let us first understand what is conditional probability. If E and F are two events associated with the sample space of a random experiment, the conditional probability of the event E, given that F has occurred, that is probability of E upon F is given by 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, we are given probability of A is equal to 0.8, probability of B is equal to 0.5 and probability of B upon A is equal to 0.4. Now, in part one, we have to find the probability of A intersection B. Now, according to our key idea, we have 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, by using this formula, we have probability of B upon A is equal to probability of B intersection A upon probability of A. Now, here we are given that probability of A is not equal to 0. So, this implies probability of B intersection A is equal to probability of B upon A into probability of A since B intersection A is equal to A intersection B. Therefore, probability of B intersection A is equal to probability of A intersection B. Since probability of B intersection A is equal to probability of A intersection B, this implies probability of A intersection B is equal to probability of B upon A into probability of A. Now, we are given probability of B upon A is 0.4 and probability of A is equal to 0.8. So, probability of A intersection B is equal to 0.4 into 0.8 and this is equal to 0.32. Now, in part two, we have to find the probability of A upon B. Now, we are given probability of B is equal to 0.5 and probability of A intersection B is equal to 0.32. Therefore, probability of A upon B is equal to probability of A intersection B upon probability of B. Now, this is equal to 0.32 upon 0.5 and this is equal to 0.64. Now, in part three, we have to find the probability of A union B and we are given probability of A is equal to 0.8, probability of B is equal to 0.5 and probability of A intersection B is equal to 0.32. 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 is equal to 0.8 plus 0.5 minus 0.32 and this is equal to 1.3 minus 0.32 and this is again equal to 0.98. Hence, the answer for part one is 0.32 for part two, it is 0.64 and the answer for part three is 0.98. So, this completes our session. I hope the solution is clear to you. Bye and have a nice day.