Most vaccines offer somewhere between 85% and 95% efficacy. Based on this efficacy, the chance of a random vaccinated individual succumbing to infection after exposure to the particular disease are 1/7 to 1/20 of the unvaccinated individual. Moreover, if the population has a sufficiently high vaccination rate, the disease can be effectively wiped out from that population so that the chance of anyone in the population being exposed and infected is practically zero.
