Liquid helium droplets of initial mean cluster size, [N], ranging from 600 to 8000 atoms are; doped with argon using the pick-up technique. The doped clusters are ionized by electron impact, and the resulting fragment ions are monitored as a function of argon pressure in the pick-up volume. Analysis of the pressure dependent ion signals is used to determine (1) the probability for charge transfer from He+ to the Ar atoms within the droplet, and (2) the probability for fragmentation of the Ar-k subclusters upon ionization. The measured charge transfer probability from He+ to Ar ranges from 0.05+/-0.02 for clusters of mean original size [N] = 8000 to 0.26+/-0.05 for [N] = 600. Charge transfer to the Ar-k constituent results in the following qualitative trends; a single Ar atom yields HenAr+ ions; Ar-2 mainly yields Ar-2(+), and Ar-3 mainly fragments to yield Ar-2(+). Simulations of the results are performed to extract information on how the charge transfer and fragmentation processes within the ionized droplet dependent on the size of the helium droplet and the number of argon atoms captured. We use the positive-hole resonant-hopping mechanism to determine that the He+ hops 3-4 times prior to localization with either the Ar dopant or another He atom to form He-2(+). This corresponds to a time scale for He-2(+) formation of 60-80 fs.