1. An urn contains three balls numbered 1, 2, and 3. Balls are drawn one at a time without replacement until the sum of the numbers drawn is four or more. Find the probability of stopping after exactly two balls are drawn.
2. A carnival huckster has placed a coin under one of three cups and asks you to guess which cup contains the coin. After you select a cup, they remove one of the unselected cups, which they guarantee does not contain the coin. You may now either stay with your original choice or switch to the other remaining cup. What decision will give you the greater probability of winning?