The question of slave uprisings is a complicated one and I'll try and answer it as succinctly as possible. (But it's going to end up running long, I know, already -- my apologies.)

First, the question as to the proportion of slaves to white people is more complicated on first blush than it appears, because it completely depends son geography and time. In the earliest of the colonial period there were few slaves and the most normative practice might be having a single slave that was much more like an indentured servant and might live with a single family and live in their home and sleep with them in the same place on a dirt floor -- but this is the earlier part of the 17th century in Virginia, for example.

As Tobacco exploded in the Chesapeake and then Rice became the fixture of South Carolina, you see a growth of slaves. In some places like South Carolina, you could have majority-slave populations in rice growing areas. But in Virginia, for example, geography dictated plantation slavery -- lots nearer the Chesapeake, far fewer in the western backcountry. So DENSITY of slaves is not going to be equal across the state or even across multiple farms -- recognizing that great planters, who could have LOTS of slaves (Washington had over 100 at his death) were far outnumbered by smaller farmers who did more subsistence farming with some small excess farming for profit with some middling planters with handfuls of slaves parked demographically in between.

So at first blush you might say: "Well, what caused all these slave snot to just overthrow their masters?" The problem (for a majority of historians of the Antebellum period, I would imagine), is that you frame the question in one in terms of numbers (ratios) alone. this is not your fault, it's just that there are far more other factors in play here.

First, there has usually been underscored a weird tension among whites who created the myth of the "happy slave" (the Sambo figure) as juxtaposed with the slave rebellion in Haiti starting in 1791 -- and specifically the white massacre in 1804 near the tail end of the rebellion and creation of an independent Haiti. So on the one hand the language and iconography of the South suggested a belief that slaves were "happy" -- including such weird and insulting phrases in planters diaries as "my darkies as happy because they are singing in the fields" -- (my pardon for the obviously offensive language of the time) with the fear of rebellion.

But most slaves didn't rebel, at least in the traditional ways of armed rebellion that we think. Slowing down the work day or other forms of passive-aggressive resistance, and even individual slaves running away for short periods only to return to plantations was more the norm.

The reasons for this are varied. Unlike in Haiti where escaped slave colonies (mawan) or "maroon" colonies in Jamaica were more possible with georgraphy, there were far fewer examples of places blacks could flee and live relatively unmolested or uncaptured. Consider: If you were on a plantation in the middle of Maryland or Virginia and rebelled, where would you run to after you killed your master? You might overpower the family that held you, but how long could you hold out against the white militias that would certainly come after? Also, realize that the reprisals for rebellion would not just be you but possibly your family -- and your family might not all live on one plantation. Whether by blood relation or kinship ties, imagine the possible consequences (real or imagined) to slaves that suspected if they rebelled.

That's not to say that rebellions did not happen -- over 200 large or small ones did. Perhaps two of the most famous that had large scope sin plans are those of Denmark Vassey in 1822 (quelled before any whites were injured) and particularly Nat Turner's rebellion in 1831 -- in that rebellion because over 50 whites died in the rebellion the retaliation of both official and vigilante justice against blacks, both those who had participated in the rebellion and those who were simply innocently murdered as a result, lead to a widespread panic. Both of these two rebellions led to stricter rules against black travel without passes from their masters and fear of slaves learning how to read, out of fear that abolitionist literature was giving slaves "ideas."

There's a lot more to it than that but that's some of the quick framework. If you'd like a VERY readable case study about a slave rebellion and the ugly aftereffects of it (which may also help explain a bit why even in places where slaves clearly outnumbered white there are other factors than numbers affected rebellion) I would suggest The Fires of Jubilee by Stephen Oates.

Again, let me emphasize what you ask is a GOOD question, it is just that ratios of blacks to whites really aren't the main thing that would be determinant of a engaging in a rebellion (or the success of one).