Fun statistical problem inside a hypothetical situation

So a friend and I were at beef obradys when the following hypothetical situation was born:

What if everyone were given a button that if pressed would give them a million dollars but would also kill one random person in the world? (And no we didn't base this of the new cameron diaz movie, we came up with this before the previews for that new movie "the box")

My questions:

1) If everyone decided to press the button (let's say a total of 7 billion people), how many people could I expect would die?

2) As the number of people in the world approaches infinity, what percentage of the population could I expect to die if everyone decides to press the button?

Things to note: everyone presses the button at the same time, the button generates a random person to die and if that person has already died no new name is selected.

Example: If there were only 2 people in the world and both pressed the button, the number of people expected to dies is 1.5