# Probability dependent event - Lottery question

Here's the question: Shrin is participating in a lottery where she's going to pull up balls from a bowl without looking at their colours. There are two white balls and eight black ones. She pulls up a ball and the colour is checked (not by her of course), and the ball is not put down in the bowl again. She gets to continue until she receives a white ball, then the game is over and she loses all her money. She gets to keep pulling out balls until she decides to quit. For each black ball she receives, one hundred dollars is given to her.

When should she quit playing the game, that is, when the risk of losing is larger than the chance of winning?

Here are my thougths: The chance of pulling two black balls is 8/10*7/9 = 62,2% But the chance of pulling three balls (8/10*7/9*6/8) is only 46.7%, therefore the risk of losing is larger than the chance of winning and she should quit after pulling two balls?

The only thing confusing me is that if you've already pulled two black balls, then the chance is still 6/8 (75%), right ? But then the answer would go down until there's only one black ball and two white ones left, and that can't be the true answer can it?