An urn contains five balls, one marked win and four marked lose. You and another player take turns selecting a ball 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 work:

a. (1/5)+(4/5)(1/5)+(4/5)(4/5)(1/5)=5/9

b. (1/5)+(4/5)(3/4)(1/3)+(4/5)(3/4)(2/3)(1/2)=3/5