Accident
Mishap
noun
An occurrence that only results because of circumstances is also called an accident. You didn't want this bad thing to happen, it was just an occurrence of circumstance! Everything aligned in the worst way.
事故 is mostly used to refer to physical accidents, like traffic accidents (交通事故) or construction accidents (建設事故). Sometimes other kinds of mishaps get the 事故 label too, like broadcast mishaps (放送事故), where something inappropriate or unplanned happens on air.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
王子を船で川の向こう岸へ渡していた時に、事故が起きたんです。
When I was ferrying the prince across the river by boat to the opposite bank, an accident occurred.
車を買ってまだ半年しかたっていないのに、もう事故に巻きこまれてしまった。
I had only owned the car for half a year, and I already got involved in an accident.
ひき逃げ事故のせいで、買ったばかりの牛肉が挽き肉になった。
Due to the hit-and-run accident, the beef he just bought became ground beef.