In 2012, a total of 224,147 women and 2,125 men in the United States were diagnosed with breast cancer (source: CDC and Prevention).As with other forms of cancer, early detection is important for breast cancer survival.The most common method for detecting the presence of breast cancer is a mammogram.Suppose a 40-year-old woman wishes to know the probability that she has breast cancer.Further, suppose she decides to have a mammogram.In 75% of all cases, if a 40-year-old actually has cancer, the mammogram will give a "positive" result.However, the mammogram will give a "positive" result 10% of the time when there actually is no cancer.Suppose we also know that 1.4% of all women who are 40 years old have breast cancer and that the probability that a mammogram will give a positive result is 0.1091.Now, suppose a woman has a mammogram and her test comes back positive.What are her chances of actually having cancer? (Round to 4 decimal places.)