well let's presume that Cheyenne is extremely unlucky and for the first 14 times she picks up a marble it's purple
14
then the next 15 times she pickes up it's pink!
14 + 15 = 29
she's picked up 29 marbles and hasn't gotten 1 green one yet, but there's only 8 green marbles left, if she needs at 3 she only has to pick up 3 more times...
14 + 15 + 3 = 32 times she needs to take out to ensure 3 green marbles.