Certainly! Let’s determine the most likely genotypes of the parents based on the criterion that all offspring are 100 percent heterozygous for plant height.
### Step-by-Step Solution:
1. Understanding Genotypes and Phenotypes:
- "T" represents the dominant allele for tall plant height.
- "t" represents the recessive allele for short plant height.
- Heterozygous means having one dominant and one recessive allele (Tt).
2. Analyzing the Possible Crosses:
- First Option: \( Tt \times Ht \)
- Assuming a typo correction as "Tt x Tt" since Ht does not represent plant height, the actual cross could be \(Tt \times Tt\).
- Second Option: \( Tt \cdot Tt \)
- Here, both parents are heterozygous (Tt).
- Third Option: \( tt \cdot t \)
- Both parents are homozygous recessive (tt).
- Fourth Option: \( TT \cdot tt \)
- One parent is homozygous dominant (TT) and the other is homozygous recessive (tt).
3. Determining the Result of Each Cross:
- Cross 1: \( Tt \times Tt \)
- Possible gametes from each parent: T, t.
- Punnett Square:
```
T t
+--------+--------+
T | TT | Tt |
+--------+--------+
t | Tt | tt |
+--------+--------+
```
- Offspring genotypes: TT, Tt, Tt, tt.
- Here, 50% are Tt (heterozygous), not 100% heterozygous.
- Cross 2: \( TT \cdot tt \)
- Possible gametes: parent 1 (T), parent 2 (t).
- Punnett Square:
```
T T
+--------+--------+
t | Tt | Tt |
+--------+--------+
t | Tt | Tt |
+--------+--------+
```
- All offspring: Tt (heterozygous).
- Cross 3: \( tt \cdot tt \)
- Possible gametes: both parents (t).
- Punnett Square:
```
t t
+--------+--------+
t | tt | tt |
+--------+--------+
t | tt | tt |
+--------+--------+
```
- All offspring: tt (homozygous recessive), none are heterozygous.
- Cross 4: \( Tt \cdot Tt \)
- This was already analyzed in cross 1 above as another interpretation.
4. Conclusion:
- The only cross that results in 100 percent heterozygous offspring (Tt) for plant height is \( TT \times tt \).
Therefore, the most likely genotypes of the parents are [tex]\( TT \cdot tt \)[/tex].
