The non-normalized wavefunction of a general qubit is given by: $$|\psi\rangle=A|0\rangle+B|1\rangle.$$ The complex amplitudes $A$ and $B$ can be represented by two arrows in the complex plane: Now the wavefunction can be multiplied by any complex number $R$ without changing the physics. This will cause the arrows $A$ and $B$ to rotate and shrink/expand together with a fixed angle between them.

Therefore two sets of points will be traced out represented by a circle with area $|A|^2$ and a circle with area $|B|^2$.

Thus if we become entangled with the qubit then the probabilities of finding ourselves in set $A$ (measuring $0$) or set $B$ (measuring $1$) are given by: $$P(0)=\frac{|A|^2}{|A|^2+|B|^2}$$ $$P(1)=\frac{|B|^2}{|A|^2+|B|^2}.$$

Does this picture help to understand the origin of probabilities in quantum mechanics?