a heterozygous organism contains one dominant gene and one recessive gene & a tay-sachs disease carrier have one dominant and one recessive tay-sachs gene ->  a tay-sachs disease carrier is heterozygous  a tay-sachs disease carrier is heterozygous & crossing two heterozygous dominant organisms causes their offspring to be homozygous recessive of 25% probability ->  the offspring of two tay-sachs carriers will have 25% probability to be homozygous recessive in tay-sachs disease  the offspring of two tay-sachs carriers will have 25% probability to be homozygous recessive in tay-sachs disease & a homozygous recessive organism contains only recessive genes ->  the offspring of two tay-sachs carriers will have 25% probability to contain only recessive genes for tay-sachs disease  the offspring of two tay-sachs carriers will have 25% probability to contain only recessive genes for tay-sachs disease & if only recessive genes are present , then the recessive trait will be visible / expressed -> the offspring of two tay-sachs carriers will have 25% probability to have the tay-sachs disease