It's possible the broken muffler could cause a misfire. Your engine is expecting a certain amount of back pressure from the exhaust. If that back pressure isn't there things may not ignite properly. It's also possible that the hole is messing with the expected gas ratio in the exhaust and the emissions control system is trying to correct it by changing the fuel/air mixture and causing a misfire.
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It's possible the broken muffler could cause a misfire. Your engine is expecting a certain amount of back pressure from the exhaust. If that back pressure isn't there things may not ignite properly. It's also possible that the hole is messing with the expected gas ratio in the exhaust and the emissions control system is trying to correct it by changing the fuel/air mixture and causing a misfire.