What are the odds of a nineteen year old having breast cancer?

< 1 in a million: The incidence of breast cancer in teenage women was recently reported as 0.08 cases per 100, 000 people, so the odds are very, very low. Regardless, any new breast lump should be followed by a physician evaluation.

VERY Low, but: It is possible, thus, a lump that persists, visualized by ultrasound, perhaps a mri, would have to biopsied to truly be determined that it was benign and not cancerous. You can't determine cancer definitively by any other test than expert pathologic diagnostic tests-- biopsy the suspect area. I know that both patients and physicians don't want to do "needless" biopsies that are benign. But........

Rare: It would be exceedingly rare.