Question

If the gardener cross-breeds two pea plants that are heterozygous, what is the probability that their offspring will have round seeds? (A) \(0 \%\) (B) \(25 \%\) (C) \(75 \%\) (D) \(100 \%\)

Short answer

The probability of the offspring having round seeds is (C) \(75\%\).

Step-by-step solution

Understand the genotype of the parents

We are given that both pea plants are heterozygous. This means they have one allele for round seeds (R) and one allele for wrinkled seeds (r). We can represent the genotype of each parent plant as Rr.

Set up a Punnett square

A Punnett square is a chart that helps us to predict the possible genotypes of the offspring when we know the genotypes of the parents. Let's set up a Punnett square for the cross between two heterozygous plants (Rr x Rr). ``` | R | r | R | | | r | | | ```

Fill in the Punnett square

Now we'll fill in the Punnett square by combining the alleles from each parent for each possible offspring genotype. ``` | R | r | R | RR | Rr| r | Rr | rr| ```

Interpret the results

We can now see the possible genotypes for the offspring. There are four squares, and three of them contain at least one R, which is the dominant allele responsible for round seeds. These genotypes are RR, Rr, and Rr.

Calculate the probability

The probability of the offspring having round seeds is the number of squares with the dominant allele divided by the total number of squares. Probability = (number of squares with dominant allele) / (total number of squares) Probability = \( \frac{3}{4} \) = \(75\%\) Based on the Punnett square and our calculations, the correct answer is (C) \(75\%\).

Key concepts

Punnett Square

The **Punnett Square** is a fundamental tool in genetics used to predict the likelihood of an offspring acquiring a particular genotype, based on the allele information of the parents. It resembles a grid where the possible alleles from each parent are placed on the rows and columns. This layout allows us to visualize and calculate the potential genetic combinations of the offspring.

• In the context of the original problem, both parents are heterozygous (Rr), which means each parent has one dominant allele (R) for round seeds and one recessive allele (r) for wrinkled seeds.


• When setting up the Punnett Square, the alleles from one parent are placed on the top, while those from the other are placed on the side.


• By filling in each square by combining one allele from each parent, we determine all possible genotypes for the offspring. In this case, the results include RR, Rr, Rr, and rr.

Understanding how to construct and utilize a Punnett Square is crucial for interpreting genetic probability outcomes.

Alleles

**Alleles** are the different forms of a gene. Every individual inherits two alleles for each gene, one from each parent. These alleles determine observable traits, known as phenotypes. Depending on their dominance, alleles can influence traits differently.

• A **dominant allele** is expressed if at least one is present. Represented by a capital letter, like R in the exercise, it masks the expression of a recessive allele.


• A **recessive allele** is only expressed when both alleles are recessive, indicated by a lowercase letter, such as r. This allele results in wrinkled seeds when paired with another r.


• Heterozygous organisms have two different alleles (Rr), showing the trait of the dominant allele. Homozygous organisms have two identical alleles, either dominant (RR) or recessive (rr).

Examining alleles helps us understand variations in genetics, especially how traits are transmitted and expressed across generations.

Probability in Genetics

**Probability in Genetics** deals with the likelihood of specific traits appearing in offspring, given the genetic makeup of the parents. It offers a way to predict the chances of inheritance patterns.

• Using a **Punnett Square**, the probability of an offspring having a particular genotype or phenotype can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is depicted as a fraction or percentage.


• For example, in our case where both parents are heterozygous (Rr), we establish the different combinations from the Punnett Square: RR, Rr, Rr, and rr. Three of these hold the dominant trait (R) for round seeds.


• The probability calculation is simple: 3 out of the 4 possible genetic combinations result in round seeds, giving us a probability of \( \frac{3}{4} \) or 75%.

Genetic probability is an essential concept for predicting how traits are inherited in living organisms, proving invaluable in fields like genetics, breeding, and ancestry research.