Stopping on the Third Draw
Combinatorics · 26th PMO Qualifying Stage
An urn contains two white and two black balls. John draws two balls simultaneously from the urn. If the balls are of different colors, he stops. Otherwise, he returns both balls to the urn and then repeats the process. What is the probability that he stops after exactly three draws?
A$\dfrac{1}{16}$
B$\dfrac{2}{27}$
C$\dfrac{1}{8}$
D$\dfrac{4}{27}$