The probability of production of dwarf offspring in a cross between two heterozygous tall pea plants can be determined using the principles of Mendelian genetics and Punnett squares.

Mendelian Genetics and Punnett Squares:
Mendelian genetics is the study of how traits are inherited from one generation to the next. It is based on the principles proposed by Gregor Mendel, who performed experiments with pea plants in the 19th century. Mendel's laws state that traits are determined by genes, and these genes are inherited in predictable patterns.

A Punnett square is a tool used to determine the possible combinations of alleles (alternative forms of a gene) that can be produced from a cross between two individuals. It allows us to determine the genotypes and phenotypes of the offspring.

Cross Between Two Heterozygous Tall Pea Plants:
In this case, both pea plants are heterozygous for the tall trait. The tall trait is dominant over the dwarf trait, where T represents the allele for tall and t represents the allele for dwarf.

The genotypes of the two parents can be represented as follows:
Parent 1: Tt
Parent 2: Tt

Creating a Punnett Square:
To determine the possible genotypes and phenotypes of the offspring, we can create a Punnett square.

T t
T TT Tt
t Tt tt

Possible Combinations:
From the Punnett square, we can see that there are four possible combinations of alleles in the offspring:

- 1 TT (tall)
- 2 Tt (tall)
- 1 tt (dwarf)

Probability of Dwarf Offspring:
Out of the four possible combinations, only one combination (tt) represents the dwarf phenotype. Therefore, the probability of producing a dwarf offspring is 1 out of 4 possible combinations, which is 1/4 or 25%.

Conclusion:
The probability of production of dwarf offspring in a cross between two heterozygous tall pea plants is 25%. This is because the dwarf trait is recessive, and both parents carry one copy of the recessive allele.