2. Given that P(A) = 2/3, P(B) =1/2 and P(AnB) =1/12. Find P(AUB). 3. If events A and B are such that they are independent and P(A) =0.3, P(B)=0.5, find P(AnB) and P(AUB). Are events A and B mutually exclusive? 4. X and Y are two events such that P(X) = 2/5. P(X | Y) =1/2 and P(Y | X) =2/3. Find (a) P(XAY). (b) P(Y). (c) P(XUY). 5. One student is selected at random from a group of 100 known to consist of 70 full-time (40 female and 30 male) students and 30 part-time (20 female and 10 male) students. Event A is "the student selected is full-time" and event C is "the student selected is female". (a) Find the probability P(AnC). (b) Find the probabilities P(A), P(C) and P(A|C). Are events A and C independent