A couple plans to have a child. The mother is homozyous for an autosomal recessive mutation, while the father is heterozygous for the same mutation. Considering this mutation, what are the potential genotypes of their offspring? Calculate the probability of each genotype occurring.

Let's assume that the autosomal recessive mutation is represented by "a" and the normal allele is represented by "A". Since the mother is homozygous for the recessive mutation, her genotype would be "aa". The father is heterozygous, so his genotype is "Aa".

The potential genotypes of the offspring can be determined by creating a Punnett square, where we will cross the mother's alleles (aa) with the father's alleles (Aa).

The Punnett square would look like this:

``` A a ----------- a | Aa | aa a | Aa | aa ```

From the Punnett square, we can see the offspring can have two possible genotypes:

1. "Aa" - heterozygous, carries the recessive mutation but is phenotypically normal.

2. "aa" - homozygous recessive, displays the phenotype of the recessive mutation.

Now, let's calculate the probabilities:

1. The probability of an offspring having the "Aa" genotype is 50%, as there are two "Aa" squares out of four.

2. The probability of an offspring having the "aa" genotype is also 50%, as there are two "aa" squares out of four.

Therefore, there is an equal 50% chance for each child to inherit the heterozygous ("Aa") genotype or the homozygous recessive ("aa") genotype with the autosomal recessive mutation from these parents.