Help with Sample Space question.

#1
Q: There are n marbles in a bag and k(k<n) of these marbles are marked.
i) Marbles are drawn from the bag at random (without replacement) until one marked marble is dawn. Write out the sample space for this experiment.
ii)The experiment is reset and this time marbles are drawn until all marked ones are found. Write out the ss for this experiment.

Ok, so i think i can do part 1 as follows: let a=the event where an unmarked marble is drawn, b=marked is drawn. Then s={b, ab, aab, aaab, ... ,aaa...ab} where the last element of the sample space repeats a n-k times.

Part 2 is where i get stuck. I know that if, say n=4, k=2 the ss looks like {bb,abb,bab,aabb,baab,abab},
but now when n=n k=k some of the ss looks like {b...b,ab...b,aab...b,aa...ab...b} however i know that this is missing elements and cant represent them.

Any help would be greatly appreciated , even if it's to tell me that I'm completely wrong!!
Thanks!!
 

BGM

TS Contributor
#2
The counting here should be similar to the idea from hypergeometric distribution; the only difference is you are requiring the last marble drawn to be marked. Not very sure is there a neat way to list out the sample space. But for sure we can know the number of elements inside.
 
#3
I also don't know a neat way to list the sample space. The sample space of the balls left in the bag in the bag is:

{empty set, a, aa, aaa ... }