Final answer:
The chance of crossing two heterozygous pea plants and having none of the four offspring showing the recessive short phenotype is 1/4 or 25%.
Step-by-step explanation:
The chance of crossing two pea plants that are heterozygous for height and have none of the four offspring showing the recessive short phenotype can be determined using the multiplication rule of probability. In this case, the two plants are heterozygous, meaning they have one dominant allele (T) for tall height and one recessive allele (t) for short height. When crossed, the possible genotypes of the offspring will be TT, Tt, Tt, and tt. Since none of the offspring can show the recessive short phenotype, the only genotype that allows for this is TT.
Using the multiplication rule, we multiply the probabilities of each event happening:
P(TT) = P(T allele from Plant 1) × P(T allele from Plant 2) = 1/2 × 1/2 = 1/4
Therefore, the chance of crossing two heterozygous pea plants and having none of the four offspring showing the recessive short phenotype is 1/4 or 25%.