Differential cross sections of positron scattering from argon atoms leading to singly and doubly charged ions were measured in the angular region from 0° to 120°. These reactions include single and double ionization, transfer, as Ps formation is referred to here, and transfer ionization. The latter is the process of simultaneously ejecting an electron and forming a positronium atom with another electron. The measurement of the time correlation between the detected ion and the scattered particle distinguishes among the reactions, resulting in Ar+ and Ar++, respectively. Measurements were carried out at 30 eV, and, mostly, at 75 eV with an estimated resolution of 2 eV FWHM. The angular acceptance ranged from ±4° to ±2°. Cross sections for single ionization are strongly forward peaked and Ps formation has the most narrow FWHM of ±12° (75 eV incident positron energy) of all. A maximum in the Ps-formation cross section away from 0°, predicted for low energies, was not observed. A very intriguing structure was observed in the transfer-ionization cross section at 45°.