Minor nitpick: the proportion of each serotype would determine the final reduction in your calculation above. If the serotypes in the 1% the vaccines don't work

Minor nitpick: the proportion of each serotype would determine the final reduction in your calculation above. If the serotypes in the 1% the vaccines don't work for are in 10% of the population of patients, then the final reduction would be to a 1:10,000 chance.