what is the probability of a 30+ woman ha ving viable eggs

The short version: no single probability exists for a 30+ woman having viable eggs; the chance depends heavily on age, and the evidence here shows the steep drop-off in egg quantity and quality.

The retrieved studies do not give a single "probability of viable eggs" number. Instead, they show the two key markers of egg supply: anti-Müllerian hormone (AMH) and antral follicle count (AFC). One study of subfertile Chinese women provides a clear age-by-age table [2]. For a 30-year-old, the average AMH was 0.69 ng/mL and AFC was 4.6. By age 35, AMH dropped to 0.36 ng/mL and AFC to 3.7. By age 40, AMH was 0.15 ng/mL and AFC was 2.9 [2]. A separate study of infertile Nigerian women found a similar pattern: the 30-39 age group had a mean AMH of 1.22 ng/mL, while the 40-49 group had a mean of just 0.63 ng/mL [1].

Egg quality also falls with age. One large study of over 6,000 embryos found that only 44% of the best-looking embryos from women under 35 were chromosomally normal. That number dropped to 21% in women 41 and older [4]. Another study of polar body testing in women with an average age of 38.6 found a 45% aneuploidy rate in oocytes [3]. So the chance that any single egg is both present and genetically normal declines sharply in the mid-to-late 30s.

My call: there is no single probability, but the evidence shows a clear and steep decline in both egg quantity and egg quality starting in the early 30s, with the most dramatic drop after 35. Confidence: high for the age-related trend, moderate for the specific numbers, which come from subfertile populations and may not apply to every woman.