A vaccine works by stimulating the immune system to produce antibodies without actually infecting someone with that disease. They trigger the immune system to produce its own antibodies as though the body has been infected with the disease. But a vaccine will not make someone immune to a disease, it will simply help the body be able fight the infection better.
If the dominant allele is t and the recessive allele ("non-taster") is n, than tn and tt are the genotypes of a "taster". tn is heterozygous and tt is dominant homozygous. nn is the genotype of a "non-taster" and it is recessive homozygous.