This paper is devoted to the influence of two types of electronic scavenger additives/compounds, namely, carbon tetrachloride (CCl4) and methyl iodide, which is also called iodomethane (CH3I), on the dielectric strength of transformer mineral oil. The tests are achieved in a sphere-sphere electrodes arrangement under AC voltage according to the IEC 60156 standard. The investigated additive concentrations range from 0 to 600 ppm. The verification of the conformity of the experimental results with normal and Weibull probabilistic distributions as well as the estimation of the breakdown voltage with risk probabilities of 1%, 10%, and 50% are also performed. It is shown that there is an optimum concentration of each type of electronic scavenger compound at which the dielectric strength of the mineral oil is significantly improved (i.e., it reaches a maximum value). This improvement is of 98% with 500 ppm of CH3I and 93% with 200 ppm of CCl4. It is also shown that the breakdown voltage values of all of the investigated samples with and without additives conform to a Weibull distribution but not to a normal distribution. The obtained results are discussed with regard to the possible mechanisms that may be responsible, particularly the two phases of inception and propagation of the streamers.