Probability › Drawing from bags › Colour ratios
Probability the game never stops
University · ●●○○○ 20 pts
A box starts with one red ball and one blue ball. At each step, a ball is taken at random from the box. If it is red, the game stops. If it is blue, it is returned to the box together with one additional blue ball. Thus, at the -th draw the box contains balls, one of which is red. Find the probability that the game never stops.