Near the end of The Hunger Games: Mockingjay Part 2, Primrose Everdeen (Katniss’ younger sister) is killed the parachute bombs President Coin’s sent over the people attempting to enter President Snow’s mansion.
My question is: Why on earth was Prim in the Capitol and not in District 13?
There are two possibilities.
As a comment already mentioned, Prim was working as a medic for the rebels (this is established earlier in the film, while they're in the underground bunker together during the Capitol's bombardment of Thirteen). Perhaps by chance she happened to be on duty at the moment when the bombs were dropped on the Capitol children, and ran to help as part of her medical team.
This is what Snow suggests when he tells Katniss it was Coin who had those bombs dropped:
"However, I must concede it was a masterful move on Coin's part. The idea that I was bombing our own helpless children instantly snapped whatever frail allegiance my people still felt to me. There was no real resistance after that. Did you know it aired live? You can see Plutarch's hand there. And in the parachutes. Well, it's that sort of thinking that you look for in a Head Gamemaker, isn't it?" Snow dabs the corners of his mouth. "I'm sure he wasn't gunning for your sister, but these things happen."
(this quote is from the book Mockingjay, but the whole rose garden conversation goes down very very similarly in the film Mockingjay: Part 2)
However, it must be borne in mind that Snow is both a hated enemy and a skilled politician. Perhaps he said "I'm sure he wasn't gunning for your sister" just to put the opposite possibility into Katniss's mind without openly endorsing it. Reverse psychology.
In the book, Katniss's internal monologue (obviously missing from the film) brings her to a different conclusion:
Suddenly, I'm thinking of Prim, who was not yet fourteen, not yet old enough to be granted the title of soldier, but somehow working on the front lines. How did such a thing happen? That my sister would have wanted to be there, I have no doubt. That she would be more capable than many older than she is a given. But for all that, someone very high up would have had to approve putting a thirteen-year-old in combat. Did Coin do it, hoping that losing Prim would push me completely over the edge? Or, at least, firmly on her side? I wouldn't even have had to witness it in person. Numerous cameras would be covering the City Circle. Capturing the moment forever.
No, now I am going crazy, slipping into some state of paranoia. Too many people would know of the mission. Word would get out. Or would it? Who would have to know besides Coin, Plutarch, and a small, loyal or easily disposable crew?
Her argumentation makes sense: Prim was enlisted as a medic for the rebels, yes, but helping wounded soldiers within the confines of Thirteen's infirmary is very different from being on the front line of the war. Could it really be chance that she just happened to be in the right place to get blown up by Coin's bombs? Even if that detail was chance, perhaps Coin intended for her to run the risk of getting killed in one way or another, either to destroy Katniss completely or to cement her loyalties to Thirteen.
Katniss's decision that Coin was truly behind the death of Prim is what drives her to kill the new president, after lulling her into complacency by saying exactly what Coin expects to hear if her plan to cement Katniss's loyalties worked. At the vote of victors on a new Capitol Hunger Games, Katniss says "I vote yes ... for Prim". Those five words are among the most important in the whole Hunger Games story. She doesn't really support a new Hunger Games, of course, but she pretends that she does in order to make Coin think that this new Katniss, while damaged, is wholly loyal to Thirteen after the death of her sister apparently at the hands of the Capitol. Then Coin has confidence in Katniss, and is completely unprepared for where her arrow really goes.
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