"Precious is very brave, because I was that strange white lady calling her and saying, 'I don't know you, but let's get together,' you know, 'Let's go out and let's talk,'" Drumwright said.
"You know, coming up with topics of conversation at first was a little bit awkward," Drumwright added. "But at the same time, she's a girl just like my daughters. And we talk about things. We talked about boys, we talked about friends, and that's the same regardless of what color somebody is."
At a local health clinic, Simpson was found to have Group B Strep, a common infection that's usually harmless in adults but can be life-threatening for newborns.
Simpson already knew something about the risks to her baby. Her sister-in-law lost a baby when the fetus got an infection in the womb.
"She wasn't going to the doctor as she was supposed to," Simpson said.
Simpson and her unborn daughter were treated with antibiotics to head off any problems. Regular trips to the clinic had eliminated at least one threat to having a healthy baby.
Simpson is not alone. So far this year, unwed mothers in Memphis had given birth to 5,188 babies -- most of them delivered at the Regional Medical Center at Memphis, a big public hospital. At "The Med," as it is called, classes are held for women and girls who have the interest and the means to visit before they're in labor.
The rate of infant mortality in Memphis would be even higher if it weren't for the work of The Med, where they save more than 1,000 babies a year who are born too early. Many of them are two, three or even four months premature.
"20/20" visited Dr. Ramasubbareddy Dhanireddy, who leads the The Med's Neonatal Intensive Care Unit, as he checked in on one baby that was born 12 weeks early and weighed only 932 grams at birth.
Dr. Sheldon Korones, founder of the neonatal unit, had a successful practice in 1968, when Dr. Martin Luther King Jr. was murdered in Memphis. The young pediatrician began campaigning for a state-of-the-art newborn center at the public hospital in the heart of Memphis' inner city to help black babies who were born poor.
"I was angry. I'm still angry," he said. "The situation hasn't changed much at all. Wherever there is a high concentration of Afro-Americans -- Washington, D.C., Memphis, Tennessee, New Orleans, you name it -- there is a higher infant mortality rate. So is it a racial issue? It seems to be preponderant among black babies, this proclivity to death."
The first city health department report warning that Memphis has a problem with infant mortality was issued in 1935. Today, every Tuesday and Thursday, as the bodies accumulate, the Health Department takes over for the families who can't afford a funeral.
"The county offers this service and most people gonna take it, because they do not have money to go to a private cemetery," said Robert Savage, a gravedigger in Memphis. "We do as better job as we can because we giving those bodies back to God."
The County Cemetery used to be called "Potter's Field." Now some people in the poor parts of town call it "Babyland."
"This is a great cemetery, and I have seen it over the years just explode, just explode with burying people," Savage said.
For now, Simpson is praying that her baby will live.