Alpha 1 anti-trypsin deficiency is an autosomal recessive genetic disorder. What are the chances that any of the offspring do not express the disease phenotype if both parents are genotype (Aa)?

The correct option is 75 per cent.

Let's break down the genetic inheritance step-by-step to understand why this is the correct answer:

1. Understanding Autosomal Recessive Inheritance
Alpha-1 antitrypsin deficiency is an autosomal recessive disorder. In autosomal recessive inheritance:
- The dominant allele is represented as:
$A$
This allele is normal and does not cause the disease.
- The recessive allele is represented as:
$a$
This allele carries the mutation for the disorder.
- An individual must inherit two copies of the recessive allele:
$\mathrm{aa}$
to express the disease phenotype.
- Individuals with genotypes:
$\mathrm{AA}$
or heterozygous:
$\mathrm{Aa}$
do not express the disease phenotype and are healthy.

2. Analyzing the Parents' Genotypes
Both parents are heterozygous:
$\mathrm{Aa}$
This means each parent has one normal allele and one mutated allele, and can pass on either allele to their offspring with a 50% chance.

3. Setting up the Genetic Cross (Punnett Square)
When crossing two heterozygous parents ($\mathrm{Aa}$ × $\mathrm{Aa}$), the possible combinations of alleles in the offspring are:
1. Dominant allele from both parents:
$\mathrm{AA}$
(unaffected, non-carrier)
2. Dominant allele from one parent and recessive from the other:
$\mathrm{Aa}$
(unaffected carrier)
3. Recessive allele from one parent and dominant from the other:
$\mathrm{aA}$
(unaffected carrier)
4. Recessive allele from both parents:
$\mathrm{aa}$
(affected by the disease)

4. Calculating the Probability
Out of the 4 possible outcomes, the genotypes that do not express the disease phenotype are:
$\mathrm{AA}$
,
$\mathrm{Aa}$
, and
$\mathrm{aA}$
(which is equivalent to $\mathrm{Aa}$). This is a total of 3 out of 4 outcomes.

We can calculate the probability as follows:

$\text{Probability}=\frac{3}{4}=75\%$

Therefore, there is a 75 per cent chance that any offspring of these parents will not express the disease phenotype.