I could really use some help with two problems:
1. A steel band is stretched tightly around the center of the Earth (the radius of the Earth is 6400 km). Then supposed the wire is cut and its length is increased by 20 m. It is then placed around the planet so that it is the same distance from the Earth at every point. Could you walk under the band? Why or why not?
2. Two hats contain red and blue marbles with the following distributions: Hat #1 has 2 red and 8 blue marbles, and hat #2 has 8 red and 2 blue marbles. Kathy selects a hat at random and randomly pulls out 2 marbles (without replacement). Both are blue. If she switches hats, what is the probability that she will now select a red marble?