Hi Marie
how to say this...if they are stupid, then they will find trouble...just like at home. they are safe to be out on the cart by themselves anywhere on the island during the day...PROVIDED they arent stupid! meaning, if they get invited to someone's house that they dont know...thats stupid. here or the US. same goes at night. If i have had too many cocktails and am walking down the street at 3am, i'm stupid...here or the US.
NOW...having said that, there is an incredibly low incident of violent crimes here on the island. the locals really do try to respect the fact that tourism makes the island.
BUT...sometimes, local boys, they can be vulgar. the girls would do well to be warned that they will get cat called, called out to, HISSED at (yes, they HISS at you), and the like. It should be handled as it would anywhere else....generally, just ignore it.
The island is a wonderful place, and i have no doubt with a little common sense (that goes for ALL travellers anywhere) everyone will absolutely have the time of their lives.
dont worry, just enjoy...it all makes sense when you are get here...
Lara
AmbergrisCaye.com 
