Understanding the Concepts

* Dominant and Recessive Alleles: Dominant alleles (represented by capital letters, like T) mask the expression of recessive alleles (represented by lowercase letters, like t). To have the recessive phenotype, an organism must have two copies of the recessive allele.

* Punnett Squares: Punnett squares are diagrams used to predict the possible genotypes and phenotypes of offspring from a cross.

Solving the Problem

1. Determine the possible gametes:

* Organism 1 (TtGg) can produce the following gametes: TG, Tg, tG, tg

* Organism 2 (TtGg) can produce the same gametes: TG, Tg, tG, tg

2. Create a Punnett Square:

| | TG | Tg | tG | tg |

|--------|--------|--------|--------|--------|

| TG | TTGG | TTGg | TtGG | TtGg |

| Tg | TTGg | TTgg | TtGg | Ttgg |

| tG | TtGG | TtGg | ttGG | ttGg |

| tg | TtGg | Ttgg | ttGg | ttgg |

3. Identify the offspring with the desired phenotype:

* We want offspring with dominant height (T) and recessive color (g). This means the offspring must have at least one "T" and two "g" alleles.

* The genotypes that meet this condition are: Ttgg and TTgg

4. Calculate the probability:

* There are a total of 16 possible offspring genotypes.

* 4 of these genotypes have the desired phenotype (Ttgg, Ttgg, TTgg, TTgg).

* Probability = (Favorable outcomes) / (Total possible outcomes) = 4/16 = 1/4

Answer: The chance of producing an offspring that has a dominant phenotype for height (T) and a recessive phenotype for color (g) is 1/4 or 25%.