Suppose the slave is a second generation African, and also herself the product of rape by a white master, and was raped by her master. In that case I think the chances the baby would be white are high. What would happen to her baby?
"White" isn't an objective standard - in the antebellum south, the child would be labelled and considered "black," and would legally be a slave, simply by virtue of having a mother who was a slave.
That said, there are isolated cases of people who were born as "black" (and as slaves) but with very pale skin managing to "pass" as white, but it was exceedingly rare for someone to be able to do that - especially if they were born into slavery.
Many slaves fit your description. For example, Sally Hemmings was 3/4ths white— she was actually Thomas Jefferson's wife's half-sister. And then she had children with Thomas Jefferson who were 7/8ths of white ancestry— and they still counted as black. That said, of Sally Hemmings' grandchildren, some were able to pass for white to enlist in the Union army, while others served in the colored troops.
(from The Hemingses of Monticello, I can find a specific quote later today...)
Even after the Civil War, by the 20th century, some states used the "One-drop rule," meaning that even a single distant ancestor who wasn't white basically disqualified your whiteness.
In response to these attitudes, Mark Twain wrote a novel in 1894 set in the antebellum south called Pudd'nhead Wilson, in which a 1/16th black slave switches her 1/32nd black son with her master's son, who as babies are impossible to tell apart. Her unknowing 'black' son grows up to be a spoiled, horrible person, while the white son grows up a slave— but when the switch is discovered, the now legally white son finds himself unable to advance or fit in in the white world, as he's completely uneducated, and speaks like a slave.