Logic Riddles

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?

Question: Two men, Watson and Holmes, are out in the extremely dry forest. They are completely surrounded by a large forest fire on one side and a dangerous cliff on the other. The wind is blowing the forest fire towards them and the cliff. The fire will reach them in about one day.

Holmes turns to Watson, "I have matches, berries, and enough water for a day. We aren't going to die." How can they avoid getting swallowed up by the forest fire?

Question: Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

Question: A natural state, I'm sought by all.
Go without me, and you shall fall.
You do me when you spend,
and use me when you eat to no end.

What am I?