You're flipping a fair coin again and again. Every time you flip heads, you add 1 black ball to a (initially empty) bag. Every time you flip tails, you add 2 re

You're flipping a fair coin again and again. Every time you flip heads, you add 1 black ball to a (initially empty) bag. Every time you flip tails, you add 2 red balls to the same bag bag. After a large number of flips, you pick a ball randomly from the bag. What are the odds that the ball was added when a heads was flipped? What are the odds that the ball is black?