What is your opinion of the idea that a single event can significantly alter the way we live our lives?
It sounds like your teacher simply wants your opinion. You can answer the question honestly, but do remember that when a teacher asks this kind of question, he or she is really wanting you to defend your opinions.
I agree with the idea that a single event can significantly alter the way we live our lives. The way that it is currently worded though makes me think that the event in question is already passed. Let me use an example. I am married. I had my wedding day, and that single event significantly changed the next eleven years. When my wife and I found out that we were pregnant, that single event changed my family dynamic forever. Those kinds of single events happen to people all of the time, and their lives are forever changed because of it.
I don't think that the question is being asked correctly though in regards to the story "A Sound of Thunder." I think the question is meant to ask how knowing about a single future action can significantly alter lives. Will you change how you live knowing that every little thing that you do can have significant repercussions?
The reason that I think the question is meant to be asked this way is because that is the question Bradbury asks in the story. Eckels steps on a single butterfly in the past, which causes massive changes back in the present. A person could go about his life attempting to scrutinize every single action and decision, but that would be pointless. Every action that he or she does or does not take will have some effect on the future, but there is no way to know exactly what the effect is. That's because the effect will feel normal. The changed present in "A Sound of Thunder" feels different because the men have something to compare it to. But in real life, you will never have the ability to shift yourself over to a different dimension and discover what the other decision wound up creating. If a person tried to micromanage every little item in order to avoid possible future cataclysmic events, that person would go crazy.
So, no I don't think knowing single events can cause drastic changes should alter how we live our daily lives.