The answer, surprisingly, is 1/2.
Perhaps more surprisingly, this answer does not depend on the particular number of employees. It would be the same if whether there were just 2 (in which case the answer is obvious) or 1000.
To see how the answer is possible, it might help to put Alfred and Zeke on the "red" team, and the other employees on the "black" team. When Alfred parks his car, he claims a parking place for red. Let's assume that this parking place actually belonged to the black team, and now consider what happens as all the other members of the black team arrive.
Nothing remarkable will happen until the person arrives whose spot has been taken. That person will have to take someone else's spot. And when that person comes, they will have to take yet another person's spot and so on. This chain of usurpation will continue until, by chance, one of the black team members takes a red spot. Then all the other black team members can park.
And then Zeke will show up looking for his spot. There were two red spots to choose from, so it's an even chance that Zeke's spot is gone or still available.
To keep things simple, we assumed that Alfred took a black team spot. What if he had not? Then we're simply saying he took a red team spot, that is, either his own or Zeke's. But he would choose either one with even odds. So in summary, there's a 50% chance that Zeke can park in his own spot.
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