Thread: Probability and Statistics Help Plz?

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.

Originally Posted by mathwiz2006

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.

In (a) you have covered the cases W, LLW, and LLLLW. But what about LLLLLLW, LLLLLLLLW, ...? Since the balls are replaced each time, the game can go on indefinitely.