In dogs, black fur (B) is dominant to white fur (b), and curly fur (C) is dominant to straight fur (c). Two parents that are heterozygous for these genes are crossed together: BbCc... In dogs, black fur (B) is dominant to white fur (b), and curly fur (C) is dominant to straight fur (c). Two parents that are heterozygous for these genes are crossed together: BbCc x BbCc. What is the chance that these parents produce offspring that are homozygous dominant for both traits?
Understand the Problem
The question is asking for the probability of offspring being homozygous dominant for both traits (black fur and curly fur) when two heterozygous dogs are crossed. To solve this, we can use a Punnett square to determine the potential genotypes of the offspring based on the given parental genotypes BbCc.
Answer
The probability of homozygous dominant offspring is $\frac{1}{16}$.
Answer for screen readers
The probability of the offspring being homozygous dominant for both traits (black fur and curly fur) is $\frac{1}{16}$.
Steps to Solve
- Set up the Punnett square
We have two heterozygous dogs that are crossed, each with the genotype BbCc. We will break down the traits into gametes. The possible gametes for each parent are:
- For Parent 1 (BbCc): BC, Bc, bC, bc
- For Parent 2 (BbCc): BC, Bc, bC, bc
We will create a 4x4 Punnett square with these gametes.
- Fill in the Punnett square
Now we fill in the Punnett square by combining the gametes from each parent.
Here's how the combinations will look:
[ \begin{array}{c|c|c|c|c} & BC & Bc & bC & bc \ \hline BC & BBCC & BBCc & BbCC & BbCc \ \hline Bc & BBCc & BBcc & BbCc & Bbcc \ \hline bC & BbCC & BbCc & bbCC & bbCc \ \hline bc & BbCc & Bbcc & bbCc & bbcc \ \end{array} ]
- Count the homozygous dominant genotypes
Next, we look for the homozygous dominant genotype, which is $BBCC$.
In the Punnett square, we see that there is 1 outcome with $BBCC$.
- Calculate total number of offspring combinations
There are 16 total combinations in the Punnett square (4 rows × 4 columns).
- Determine the probability
The probability of getting a homozygous dominant offspring for both traits is calculated by taking the number of homozygous dominant outcomes and dividing it by the total number of offspring combinations:
$$ P(BBCC) = \frac{\text{Number of } BBCC}{\text{Total combinations}} = \frac{1}{16} $$
The probability of the offspring being homozygous dominant for both traits (black fur and curly fur) is $\frac{1}{16}$.
More Information
In this particular genetic scenario, both traits are independently assorted according to Mendelian genetics. This illustrates the basic principles of inheritance and can serve as a basis for understanding more complex genetic scenarios.
Tips
- Forgetting to include all possible gametes: Ensure that each parent’s gametes are fully considered in the Punnett square.
- Miscounting the number of desired genotypes in the Punnett square: Carefully verify each box in the square to avoid mistakes in counting.
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