Trusting God is less about 'i'm sure God won't let this bad thing happen', though there may be times when that Is the case, but it's more about trusting God to help us when the troubles come.
If you read in the bible, you will see many people, OT and NT, that suffered, often for the sole reason that they followed God.
So, i suppose you could say, it's less about trusting God to prevent bad things, and more about trusting in Him to get you through the bad times, and in such a way that some form of good comes from it. Because we live in an evil, fallen world. And like it or not, we are subject to the sins, not only our own, but the sins and actions of others. We are subject to our own consequences, such as not studying for a test. You reap what you sow, as the bible says. When you don't study, you don't get a good grade. This is a Natural consequence.
But keep in mind, when we get consequences, we have the choice to be mad at God for letting us fail when we didn't study, or we can learn from our consequence and realize that it was OUR fault, not Gods, and learn that we need to study. Studying is just one example, this applies to life in general.
The bible is full of martyrs, people who went to prison, slavery and other such things. These were Gods followers. But God sustained them all.
You can also trust God in other ways as well, such as when you put your trust in Him to save you.
Just keep in mind, Gods goal in our lives is not to prevent bad, but to cause us to grow as people, as Christian and in our relationships with Him. It's not all about 'us' but it's all about 'Him'. You don't hear that taught a lot anymore, as so much modern Christian teaching sounds more like self help and having it all about you. The bible teaches to have a giving heart, to be a servant by choice, it does not teach that our happiness is the goal in life, but rather our growth is the goal.