Math Riddles

Question: Does a ton of feathers or a ton of bricks weigh more?

Question: There are two ropes that both take exactly 1 hour to burn from end to end. You are unable to cut the rope. How can you burn the two ropes in a total of 45 minutes?

Question: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?

The glass is a right cylinder.

Question: If you have 30 white socks, 22 black socks, and 14 blue socks scattered across the floor in the dark, how many would you have to grab to get a matching pair?

Question: There are 100 passengers boarding a 100 passenger airplane. When passenger 1 gets onto the plane, he is dissoriented, so he randomly picks a seat. Each of the remaining passengers (2, 3, 4, etc.) get onto the plane and take their seat if it is available or picks one of the remaining seats at random if it is not.

What is the chance that the last passenger (passenger 100) will get his seat?