As gum blossom said, possible yes, but it can be extremely difficult. Yes, some women are extremely fertile until 50. But, most women have a severely dimisnished fertility. I think this article sums it up well:
http://newsblogs.chicagotribune.com/triage/2008/04/your-biological.html
"Until age 34, women have a 20 percent chance of conceiving in a given month and 20 percent of those pregnancies will end in a miscarriage.
After 35, a woman’s likelihood of conceiving in a given month drops to 10 percent and her miscarriage risk goes up to 30 percent.
After 40, she has a 5 percent chance of getting pregnant and a 40 percent chance of having a miscarriage.
After 42, “99 percent of fertility is over,” Lederer said".
And, yes, the chance of miscarriage also skyockets once you get older. I know all about that.
If you want to have a baby, start now and I'd start immediately with an RE to have them run some tests to see where your fertility is at. I'd also expect to have some medical intervention, but who know, maybe you'll be one of the lucky ones.
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