The cops can't get anywhere near the building without getting blown to s**t. But John McClane is nothing if not resourceful: He grabs a load of C-4 explosive that he borrowed from a dead terrorist, secures it to a chair using an old school computer monitor and drops it down an elevator shaft. What follows is one of the great moments in classic cinema:
The C-4 explodes upon impact at the floor where the missile-launching terrorists are, killing them and making the building a little less insanely dangerous. Thank God for John McClane, right?
The Blind Luck:
How did McClane know the C-4 would explode on that exact floor? He is on the 38th floor when he drops the explosives, and the hostages (including his wife) are on the 30th or so. He doesn't have a detonator switch to set the bomb off, so how did he know the chair would blow on the terrorists' floor as opposed to, say, landing on an elevator and getting carried up to some other random floor (like, say, the one where all the hostages are)? Hell, what's to say it doesn't bounce off the walls of the shaft at some point on the way down, blowing some key structural support and bringing the whole building down? Or at least a huge part of it?
Or, best case scenario, it goes straight to the basement and kills Argyle.
McClane does briefly look down the shaft to make sure the coast is clear, presumably, but one thing elevators tend to do is move up and down in a matter of seconds; he knows there are terrorists using the elevators because he just heard them. In fact, that's his entire knowledge of the situation: He heard an elevator go past, and from that somehow assumed that a) it had to be boarded by the terrorists who would later shoot those missiles and b) they stopped close enough to the ground level that the explosion wouldn't do any serious damage on the top floors where all the innocent people are.
"So ... dyin' hard or hardly dyin'?"