Because one of my family died of cancer, does that mean I have a bigger chance of dying of cancer as well?It was my grandma that died of cancer if that helps.
One of the things that predisposes a person to having cancer is a family history of the occurence of cancer. Since your grandmother died of a particular type of cancer, that gives you a family background with an occurence of cancer. It raises the possibility that you might die of cancer, but one occurence within your family usually isn't enough to pass that kind of judgment.
There are lots of different kinds of cancer. There are forms that are treatable with good success rates and those that are not. Your grandmother might have participated in a lifestyle selection, such as smoking cigarettes, that made her more likely to develop cancer. I would say at this point, educate yourself on the subject of cancer, be aware of the causes of cancer. Don't worry about this one known occurence within your family, at least for now. Yes, it increases your chances, but not by that much; there are simply too many factors playing an influence.