- 37

- 0

**1. Homework Statement**

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

**3. The Attempt at a Solution**

(a) P(W) + P(LW) + P(LLW) + . . . . .

(1/5) + (4/5)(1/5) + (4/5)(4/5)(1/5) . . . .

so its is a series

SUM (1/5)(4/5)^(n-1) starting at n=1 to infinity

when I did this I got 1 and not 5/9

(b) P(W) + P(LW) + P(LLW) . . .

(1/5) + (4/5)(1/4) + (4/5)(3/4)(1/3) . . ..

SUM (1/5)( . . . and I got stuck here

Any Help would be appreciated

Thanks