Problem Analysis:
The task involves determining the genotypes of Theodore and Merin based on their phenotypes, completing a Punnett square for their offspring, and calculating the probability of their offspring having specific traits. Additionally, we need to determine the probability that Gandalf and Love-Merlin will have a baby who cannot fly.
#### Step 1: Determine Theodore's and Merin's Genotypes
-
Theodore: Can fly and has normal skin.
- The gene for flying is dominant (`F`), so Theodore must have at least one `F` allele.
- The gene for normal skin is recessive (`n`), so Theodore must have two `n` alleles.
- Therefore, Theodore's genotype is
Fnn.
-
Merin: Cannot fly and has spotted skin.
- The gene for flying is dominant (`F`), so Merin must have two recessive alleles (`ff`) for not being able to fly.
- The gene for spotted skin is dominant (`N`), so Merin must have at least one `N` allele.
- Therefore, Merin's genotype is
ffNn.
#### Step 2: Complete the Punnett Square for Theodore and Merin
We now create a Punnett square using Theodore's genotype (`Fnn`) and Merin's genotype (`ffNn`).
| | Fnn (Theodore) |
|-----|----------------|
| fN | fFNn |
| fn | ffnN |
#### Step 3: Determine the Phenotypes of the Offspring
-
fFNn: Can fly (dominant `F`) and has normal skin (recessive `nn`).
-
ffnN: Cannot fly (recessive `ff`) and has spotted skin (dominant `N`).
#### Step 4: Calculate the Probability of Non-Flying Offspring
From the Punnett square:
- There are 2 possible combinations: `fFNn` and `ffnN`.
- Only `ffnN` represents an offspring that cannot fly.
- Therefore, the probability of non-flying offspring is
50%.
#### Step 5: Determine Gandalf's and Love-Merlin's Genotypes
-
Gandalf: Can fly and has green skin.
- The gene for flying is dominant (`F`), so Gandalf must have at least one `F` allele.
- The gene for green skin is recessive (`gg`), so Gandalf must have two `g` alleles.
- Therefore, Gandalf's genotype is
Fg.
-
Love-Merlin: Cannot fly and has no skin.
- The gene for flying is dominant (`F`), so Love-Merlin must have two recessive alleles (`ff`) for not being able to fly.
- The gene for no skin is recessive (`gg`), so Love-Merlin must have two `g` alleles.
- Therefore, Love-Merlin's genotype is
ffgg.
#### Step 6: Calculate the Probability of Their Baby Not Being Able to Fly
Since Love-Merlin has the genotype `ffgg`, she cannot fly. Gandalf's genotype is `Fg`, which means he can fly but carries the recessive allele for green skin. However, since Love-Merlin has two recessive alleles for flying (`ff`), all their offspring will inherit one `f` allele from her and one `f` allele from Gandalf, resulting in the genotype `ff`.
Thus,
all their offspring will be unable to fly. The probability is
100%.
Final Answer:
$$
\boxed{100\%}
$$
Parent Tip: Review the logic above to help your child master the concept of dihybrid cross problems worksheet.