Final answer:
To calculate the expected number of seeds that germinate, consider the genetic probability of seed traits based on Mendel's laws. For pea plants, a 3:1 ratio implies a 75% chance for round seeds in F₂ generation. Multiplying this probability by the total number of progeny (e.g., 810) gives the expected number of germinated round seeds, which is 607.500 when rounded to three decimal places.
Step-by-step explanation:
To determine what is the expected number of seeds that germinate, we need to consider the genetic probability of certain traits being expressed in offspring, as per Mendel's laws. For example, in the case of the garden pea plants involving seed texture, when crossing true-breeding round seeds with wrinkled seeds, we obtain F₁ offspring that are expected to be all round because of dominance. These F₁ plants when self-crossed (F₂ generation) have a 3:1 ratio of round to wrinkled seeds, which is a 75% (or 0.75) probability for round seeds. Thus, in an F₂ progeny population, for every four seeds planted, we expect three to germinate as round seeds. If we take the given example data of 810 as the total number of F₂ progeny, multiplying by the probability of 0.75 for round seeds, we can calculate the expected number.
Expected number of round seeds that germinate: 810 × 0.75 = 607.5
Rounding to three decimal places, we get 607.500 as the expected number of germinated round seeds.