Tay–Sachs is an inherited disease caused by a recessive allele lowercase t. The Punnett square shows the genotypes of a male and female and the predicted genotypes for their offspring. What is the probability in percent that a child born to these parents will inherit Tay–Sachs disease?
Let’s start by reviewing some key terms. A gene is a sequence of DNA that contains the information needed to produce a certain characteristic, for example, eye color. Alleles are different versions of a gene. For example, for an eye color gene, there might exist an allele for blue eyes and an allele for green eyes. And alleles can be either dominant or recessive. A dominant allele is one which will always be expressed if it’s present in an individual. A recessive allele is one which is only expressed in an individual if no dominant allele for that gene is present in that individual.
Dominant alleles are notated as uppercase, or capital, letters. So for the gene G, a capital G would indicate the dominant allele for that gene. Recessive alleles, on the other hand, are notated by lowercase letters. So a lowercase g would indicate the recessive allele for the gene G. In humans, as well as many other organisms, an individual will have two alleles for each gene, and the specific combination of alleles that an individual has is known as that individual’s genotype. A child will receive one allele from each parent, that is, one from the father and one from the mother. Together, these two alleles would make up the child’s genotype, in this case, uppercase G uppercase G, also known as homozygous dominant.
A Punnett square is a useful tool for determining potential genotypes and the probabilities of those genotypes in the offspring of a particular pair of parents. It’s important to note that the probabilities that we find with the Punnett square are probabilities of these genotypes for each child of the parents, not necessarily what we would be sure to see in a group of four children from these parents. So according to this Punnett square, each child of these parents would have a one-out-of-four, or one-quarter, chance of inheriting the uppercase T uppercase T genotype since only one out of the four boxes in the Punnett square contains this genotype.
Likewise, each child would have a two-out-of-four, or one-half, chance of inheriting the uppercase T lowercase t genotype since two out of the four boxes in the Punnett square show this genotype. And each child will also have a one-out-of-four chance of having the lowercase t lowercase t genotype since only one out of the four boxes contains that genotype. So in the question, we’re told that Tay–Sachs is caused by a recessive allele lowercase t. Which of these genotypes contains that lowercase t allele? Both of these genotypes contain a lowercase t.
However, remember that when we have a dominant allele, such as the uppercase T, that the dominant allele will be expressed while the recessive allele will not. So in this case the disease-causing recessive lowercase t allele will not be expressed in the genotype uppercase T lowercase t. And so offspring with this genotype will not inherit Tay–Sachs disease. The only offspring that will inherit Tay–Sachs disease are those with the lower case t lowercase t genotype, or homozygous recessive genotype. And each child of these parents has a one-out-of-four, or one-quarter, chance of inheriting this genotype.
So we know that the probability that a child inherits Tay–Sachs is one out of four, or one-quarter. But the question asked about the probability in percent, so we can multiply one over four times 100 percent to get 25 percent. Or we can just remember that a quarter of 100 percent is 25 percent. Either way, we can determine that the probability in percent that a child born to these parents will inherit Tay–Sachs disease is 25 percent.