Question 243396
If she needs to be guaranteed, then the probability has to be 100%


The tub contains 5 black, 4 brown, 3 white.


Worst case possibility is she gets a different one each time.


Let a = black, b = brown, c = white


She gets:


abc abc abc


Each letter is a draw.


On the seventh draw she has to get 3 of the same color.


Let's assume she gets 2 of the same color in a row.


Each letter is a draw.


aabbcc aabbcc


On the 7th draw she has to get 2 of the same color.


I don't believe there is a worse case then that, so if she absolutely has to be guaranteed that she has 3 buttons of the same color, she would have to draw a minimnum of 7 times.


In terms of probability, the probability becomes 1 on the 7th draw.


This would be a conditional probability.


Given that she has drawn 2 black, 2 brown, and 2 white, the probability that swhe will draw the third black or brown or white on the 7th draw becomes 1.