This is Statistics, please show all work, thank you!

Consider the following probability space. S = {DG+, DG-, Dg+, Dg-}, 0.64 if x = DG+ P({x}) = 0.20 if x = DG- 0.08 if x = Dg + or Dg- a.) Verify that P is a valid probability function on S. b.) Consider the even A that there is a "+" in the outcome and the event B that there is a g in the outcome. Using the probability function defined in (a), calculate P(A), P(AUB), and P(A|B). (Note: you can leave your answer as a sum or product of fractions. No need to simplify or calculate decimal values.) c. ) Are the events A and B defined in part (b) independent