A postmenopausal woman with a solitary painless irregular breast lump is most likely diagnosed with?

In a postmenopausal woman, the presence of a solitary, painless, irregular breast lump raises concerns for breast cancer. The most common histological type of breast cancer in this demographic is invasive ductal carcinoma (IDC). IDC typically presents as an irregular mass on examination and can be asymptomatic, which aligns with the case's description of a painless lump.

Postmenopausal status is particularly significant because hormonal changes can influence the likelihood of breast malignancies. The risk of breast cancer increases with age, particularly after menopause, making it important to consider IDC in this context, given its prevalence.

Invasive lobular carcinoma is another form of breast cancer, but it tends to present with a different clinical picture and often manifests as a more subtle thickening rather than a distinct mass. Fibroadenomas, on the other hand, are typically found in younger women and tend to be mobile and painful rather than presenting as an irregular lump in a postmenopausal cohort. Mucinous carcinoma, while a subtype of breast cancer, is less common and would not be the most likely diagnosis in the scenario described.

Hence, based on the woman's age, menopausal status, and the characteristics of the lump, invasive ductal carcinoma is the most probable diagnosis