Was Prim's selection rigged?

As we all know, Prim was originally selected to be the District 12 Female Tribute for the 74th annual Hunger Games.

However, here's the problem:

1. Prim only had one entry into the Games.


2. There were at least a few thousand more people that could have been picked.

It's a statistical improbability that Primrose would have been picked, therefore (slightly) implying that her entry into the game was rigged due to some factor (Possibly Katniss' troublemaking by sneaking into the forest?).

So, was Prim's entry rigged, or was it just terrible luck? If the entry was rigged, why?