Online security issues continue to grow as a concern, amplified by the coronavirus pandemic. The current cohort of young people (aged 18 -30, "Generation Z") are the first to have grown up with digital technologies, but to what extent are they worried about online security attacks and what experience do they have of them? An online survey of 81 young UK participants investigated their experience with 12 scenarios presenting online security attacks, asked about their level of worry with 9 online security attacks and their knowledge of computer and online security, and their confidence in their ability to identity an attack. Experience with the online attacks ranged widely, from over 50% of participants experiencing spear phishing to attempt identity theft, to only 2.5% experiencing a spoofed website. A principal components analysis showed that worries clearly fell into two components: Theft Worry and Phishing Worry. Levels of worry on these two components could be predicted from the number of different online security attacks participants had experienced. These relationships may be useful for developing education and advice to encourage better online security behaviour.