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?
Answer: There is a 50 percent chance.
When the last passenger gets on seats 2 - 99 will be taken for sure. Each of these passengers would take their seats if they were available, so the only seat remaining at the end would be 1 or 100. So there is a 50 percent chance that passenger 100 would get seat 100.
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.
Answer: Tip the glass of water until the water reaches the rim of the glass and if the water lines up perfectly with the bottom rim of the glass, it is half full.