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
Hello, antman!
I too agree with your answers.
and I think I know how you got .
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
For (a), I believe you meant to type: .
The geometric series has sum: .
. . Therefore: .
If that is the case, you did terrific work on both parts.
. . Nice going!