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 - answer = 5/9
(b) without replacement - answer = 3/5
(a) 1/5 + [(4/5)(4/5)(1/5)] + [(4/5)(4/5)(4/5)(4/5)(1/5)] = 1281/3125
(b) 1/5 + [(4/5)(3/4)(1/3)] + [(4/5)(3/4)(2/3)(1/2)(1/1)] = 3/5
I was able to solve (b) with no problem . For (a) I did the same thing except took replacement into consideration, but keep getting 1281/3125
Please help explain what I am doing wrong.