That's not *too* far from the truth.

You can always describe the probabilities of a two-outcome event like that: you have $p_1+p_2=1$ and thus defining $c_i\equiv\sqrt{p_i}$ you observe that $(c_1,c_2)$ are distributed on a circle (more precisely, in the upper-right sector of one).
More generally, if an event has $n$ possible outcomes, you can describe the corresponding probabilities as the squares of the components of points on (one sector of) a hypersphere: $p_i\equiv c_i^2$ with $(c_i)_{i=1}^n\equiv\boldsymbol c\in S^{n-1}$.

Note that this has nothing to do with quantum mechanics, it's just something that follows from the mathematics on any probabilistic description of an event.

The question is, why would you ever want to do this? The answer is that, in QM, it turns out that describing states in the terms of the coefficients $c_i$ (let's call these *amplitudes*) is simpler. However, it also turns out that using values $c_i\in[0,1]$, as is the case when you define these as square roots of probabilities, is not sufficient to fully describe quantum states. This can be fixed by "promoting" these coefficients to be *complex numbers*, $c_i\in\mathbb C$.
In the case of a qubit, this amounts to the state being describable as a point on *a sphere*, rather than on a circle (the complex phases add an additional "phase angle" on top of the "angle" corresponding to the measurement probabilities).

In summary, yes you can naturally associate to every point on a circle (a hypersphere) a qubit (qudit). The inverse relation will not hold however: there are more quantum states than those describable in such a way.
It might be worth noting that if you are only interested in what happens in a single measurement basis, then you have a one-to-one relationship between your circle and the possible outcome probabilities. This is to be expected, as if you do not work with different measurement bases, everything can be described with classical probability theory.

1you can include math using the

`$`

delimiters. E.g.`$a^2+b^2=1$`

renders as $a^2+b^2=1$ – glS – 2020-05-08T15:54:38.9001

You're not quite right, but this concept is very similar to the Bloch sphere: https://en.wikipedia.org/wiki/Bloch_sphere

– probably_someone – 2020-05-09T00:52:56.057