Question

the leaders of austria-hungary declared war on the country of serbia after archduke franz ferdinand was shot. why?
they hoped that declaring war on serbia would start
a worldwide war.
the assassination, or murder, of the archduke
happened in serbia.
they blamed the serbian military for helping gavrilo
princip.
they thought that serbia was going to declare war.
so, they decided to declare war first.

Explanation:

The assassination of Archduke Franz Ferdinand by Gavrilo Princip (a member of the Serbian nationalist group Black Hand) led Austria-Hungary to blame Serbia. Austria-Hungary accused the Serbian military of aiding the assassin, which was their key justification for declaring war. Other options are incorrect: they did not aim to start a world war (it was an unintended outcome), the assassination occurred in Sarajevo (then part of Austria-Hungary, not Serbia), and there was no evidence Serbia planned to declare war first.

Answer:

They blamed the Serbian military for helping Gavrilo Princip.