My mother has an aortic aneurysm. What is the chance that I will also get this?

AAA. When aortic aneurysms affect a female in your family you have an increased likelihood for AAA. You can diminish your risk as opposed to increasing your risk by never smoking and controlling your blood pressure. You are too young for AAA screening by ultrasound. If other relatives have AAA get screened in the future as your physician recommends.
Depends. There are multiple risk factors for abdominal aortic aneurysms. The biggest risk factors are being a male smoker over the age of 65. Family history is also a risk factor and should prompt you to have your aorta evaluated with by an ultrasound exam.
Age dependent. As a first degree relative you should be screened at the age, five years before your mother was diagnosed, or at any time if you have symptoms.