Did President Coin Kill Prim?

In Mockingjay, Prim dies from President Coin's bombs and later Katniss votes to have The Games continue.

Why does President Coin killed Prim?

Coin couldn't control her and she was no longer useful as the symbol for the rebellion, so she wanted her out of the way. Destroying the thing she loves most was her attempt to make her either careless about her own life or to go more or less insane.

Why did snow laugh when Katniss kill Coin?

But, before his death, after Katniss kills Coin, Snow breaks out into a fit of laughter. ... Snow laughs because he enjoys the irony of the situation. He avoids the official execution ceremony, even though Panem's citizens still take their revenge on him.