How can an offspring inherit a recessive trait ?

Is it when both parents carry that trait?

In the plant shown (plant is an orchid with equal numbers of small white and purple specs on each petal) , the allele for the purple flower color is most likely:
Dominant, recessive, codominant, or incompletely dominant with the allele for the white flower color ?
I think it is codominant.
Please answer ?

yes.

RrxRr= RR, Rr, Rr,rr

codominant.

To understand how an offspring can inherit a recessive trait, it is important to understand the basics of genetics. Inheritance of traits is determined by the combination of alleles, which are different forms of genes. Each individual has two alleles for each gene, one from each parent.

For a recessive trait to be expressed in an offspring, both parents must contribute a copy of the recessive allele. This means that both parents must carry the recessive allele, even if they do not exhibit the trait themselves.

In the case of the orchid plant example you provided, where there are equal numbers of small white and purple specks on each petal, we can infer the most likely inheritance pattern based on the given information.

If the allele for the purple flower color is dominant, then the offspring would only display the purple flower color if they inherited at least one copy of the dominant allele from one of the parents.

If the allele for the purple flower color is recessive, then the offspring would only display the purple flower color if they inherited two copies of the recessive allele, one from each parent.

If the allele for the purple flower color is codominant, then both alleles for purple and white flower colors would be expressed equally in the offspring. This means that the offspring would have both purple and white specks on their petals.

If the allele for the purple flower color is incompletely dominant with the allele for the white flower color, it means that one allele is not completely dominant over the other. In this case, the offspring would have a mix of both purple and white specks on their petals, showing an intermediate phenotype.

Based on the information given, it is difficult to determine with certainty which inheritance pattern is the most likely. Further information would be needed to make a definite conclusion.