Do vegetarians have less of a probability statistic to develop cancer of the breasts?

Depends. Increase in breast cancer is linked to genetics, obesity, too much alcohol (drinking more that 7 per week), smoking, high fat diets, and pregnancy after 30. So if you are a vegetarian but have some of these risk factors, then you are not protected any more than the rest of the populations. Eating more plant based can help increase nutrient from food and decrease calories.
Little evidence here. All retrospective studies generate a lot of noise and associations that aren't cause-and-effect, and you should only pay attention to findings that are strong and consistent. The biggest studies have shown no advantage for vegetarians in longevity or any category of illness when we control for other factors; even if true, the case is weak <a href="