Answered

In guinea pigs, short hair [tex]$(S)$[/tex] is dominant over long hair [tex]$(s)$[/tex]. If a short-haired [tex]$(Ss)$[/tex] guinea pig is crossed with a long-haired [tex]$(ss)$[/tex] guinea pig, what are the possible genotypes and phenotypes of their offspring and the percent chance of each?

Chance [tex]$= \frac{\# \text{ of offspring with Genotype (or phenotype)}}{4}$[/tex]

[tex]\[
\begin{array}{lll}
1.00 = 100\% & 0.75 = 75\% & 0.50 = 50\% \\
0.25 = 25\% & 0.00 = 0\%
\end{array}
\][/tex]

\begin{tabular}{|l|l|l|l|}
\hline
Genotype & Chance (\%) of Offspring w/ Genotype & Phenotype & Chance (\%) of Offspring w/ Phenotype \\
\hline
Ss & 50\% & Short hair & 50\% \\
\hline
ss & 50\% & Long hair & 50\% \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's analyze the genetic cross between a short-haired guinea pig (genotype [tex]\(S_\)[/tex] or possibly [tex]\(SS\)[/tex] or [tex]\(Ss\)[/tex]) and a long-haired guinea pig (genotype [tex]\(ss\)[/tex]). For simplicity and common practice, we assume the short-haired guinea pig is heterozygous [tex]\(Ss\)[/tex], as dominant traits are most informative when considering heterozygous crosses.

### Step-by-Step Solution:

1. Identify the parent genotypes:
- Short-haired guinea pig: [tex]\(Ss\)[/tex]
- Long-haired guinea pig: [tex]\(ss\)[/tex]

2. Determine the possible gametes:
- The [tex]\(Ss\)[/tex] parent can produce gametes with [tex]\(S\)[/tex] or [tex]\(s\)[/tex].
- The [tex]\(ss\)[/tex] parent can produce gametes with [tex]\(s\)[/tex] only.

3. Set up the Punnett square:
```
S s
----------------
s | Ss | ss |
----------------
s | Ss | ss |
----------------
```

4. Identify the genotypes of the offspring:
- From the Punnett square:
- 50% chance ([tex]\(2/4\)[/tex]) for [tex]\(Ss\)[/tex]
- 50% chance ([tex]\(2/4\)[/tex]) for [tex]\(ss\)[/tex]

5. Determine the phenotypes of the offspring:
- [tex]\(Ss\)[/tex] results in short hair (dominant trait).
- [tex]\(ss\)[/tex] results in long hair (recessive trait).

6. Calculate the chance percentages:
- For genotypes:
- [tex]\(Ss\)[/tex]: 50%
- [tex]\(ss\)[/tex]: 50%
- For phenotypes:
- Short hair ([tex]\(Ss\)[/tex]): 50%
- Long hair ([tex]\(ss\)[/tex]): 50%

### Result Summary:
```plaintext
Genotype | Chance (%) of Offspring w/Genotype | Phenotype | Chance (%) of Offspring w/Phenotype
---------------------------------------------------------------------------------------------------------
Ss | 50% | Short hair | 50%
---------------------------------------------------------------------------------------------------------
ss | 50% | Long hair | 50%
---------------------------------------------------------------------------------------------------------
```

Each possible genotype and phenotype has been calculated step-by-step to ensure accuracy. This setup ensures you know the potential outcomes for the offspring of the genetic cross.