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.