As a parent, do you reserve the right to snoop on your child if you have concerns?

I have my mom's same views on this. If you live in my home, use the electricity that I pay for, eat the food that I buy, wear the clothes that I have provided for you, use my furniture, sleep in the bed that I bought... then I reserve the right to go through your things if I have concerns. I would have no problem going through their phone, emails, drawers, closets, purses, bags etc. My mother just went through my things randomly, which is probably a good thing. I wasn't a very sneaky child, I always got caught doing bad things, such as smoking cigs. I was 16 when she found cigs in my purse. She threw them all away but one ,and she put that one on my computer keyboard for about 4 months. Once a week she would come down to make sure it was still there. I was so petrified, I never smoked again. She never read my journal, and I would never read my child's personal thoughts, unless I thought my child was doing something terrible (drugs, , gangs, stealing, lying etc.). Once my children are out on their own, then I absolutely will not not be going through their things, UNLESS I thought they were doing something pretty bad such as drugs, stealing etc... especially if they have children of their own.