An urn contains 5 balls, one marked WIN and four marked LOOSE. You and another player take turns selecting a ball at random from the urn, one at a time. The first person to select the WIN ball is the winner. If you draw first, find the probability that you will win if the sampling is done (a)With replacement; (b) Without replacement.
My initial thought was that a would simply be 1/5. We're replacing the balls so every time we draw, it's like we have a clean slate, or as if we are only drawing one time. My professors solution sheet has the answer for part a) as 5/9. I have no clue how he got there. Part b) I honestly don't know where to start.