Predicting Monohybrid Inheritance with Punnett Squares and Probability

Hello! Last lesson followed how an mRNA sequence determines the amino acid sequence of a polypeptide. This lesson shifts to a different question about genetic information: which version of a gene might an offspring inherit from each parent? You’ll use Punnett squares and probability to predict outcomes for a single gene. Allow about 35–40 minutes for the lesson, video and selected reading.

From alleles to observable traits

An allele is a version of a gene. For the single gene considered in a monohybrid cross, an offspring inherits one allele from each parent. Its pair of alleles is its genotype; the observable characteristic is its phenotype. These are not interchangeable: two offspring can have different genotypes but the same phenotype.

In the simple dominant–recessive model used here, we write a dominant allele with a capital letter and a recessive allele with the corresponding lowercase letter. Suppose $Y$ produces yellow pea seeds and is dominant to $y$, which produces green seeds. The three possible genotypes have these meanings:

Homozygous means the two alleles are the same; heterozygous means they differ. In this model, an offspring needs two $y$ alleles to show the recessive, green phenotype. A yellow seed, however, could have either $YY$ or $Yy$. Dominance tells you how alleles affect the phenotype—not which allele an offspring is more likely to inherit.

Read the opening of OpenStax’s Characteristics and Traits for the distinction between genotype and phenotype and the meaning of dominance.

The model matters. Not every characteristic follows simple complete dominance, so use a capital–lowercase interpretation when the question states or establishes that inheritance pattern.

A Punnett square represents possible fertilisations

To predict offspring, first work out what allele each parent can place in a gamete—an egg or sperm cell. When the alleles separate during meiosis, a $Yy$ parent can produce gametes carrying $Y$ or $y$. For this simple cross, each has a probability of $\frac{1}{2}$. A $yy$ parent produces only $y$-carrying gametes.

A Punnett square pairs every gamete possibility from one parent with every possibility from the other. Watch Nicole Lantz’s Probabilities and Punnett Squares to see the setup before you read the cells as probabilities.

Consider a cross between a heterozygous yellow-seeded plant and a green-seeded plant: $Yy\times yy$. Put one parent’s possible gametes across the top and the other’s down the side:

The two $y$ row labels are deliberately identical: the $yy$ parent can supply only $y$. Repeating that label makes a four-cell grid convenient; it does not mean this parent has two different gamete types.

Two cells contain $Yy$ and two contain $yy$. Thus the predicted genotype ratio is $1Yy:1yy$, and the phenotype ratio is $1$ yellow:$1$ green. Each phenotype has a $\frac{1}{2}$, or $50\%$, probability for an offspring.

Now change the parents to $Yy\times Yy$. Each can supply $Y$ or $y$, so the square is:

There are two routes to $Yy$: one parent can supply $Y$ while the other supplies $y$, or their contributions can be reversed. Count both cells. The resulting genotype ratio is $1YY:2Yy:1yy$. Because $YY$ and $Yy$ are both yellow, the phenotype ratio is $3$ yellow:$1$ green.

Read the corresponding crosses in OpenStax to connect the grid to segregation into gametes. Stop before the article moves on to further crosses.

The contrast is important for exams: $3:1$ is not the ratio for every monohybrid cross. It results from two heterozygous parents under this dominance model. You must establish the parental genotypes before predicting a ratio.

Why the square agrees with probability

A Punnett square is a visual probability calculation. In the $Yy\times Yy$ cross, an offspring is $yy$ only if one parent supplies $y$ and the other also supplies $y$. Each contribution has probability $\frac{1}{2}$; for these independent contributions, multiply:

This is the product rule, useful when both specified events must happen. In the four-cell square, the $yy$ cell represents that same $\frac{1}{4}$ probability.

For a yellow offspring, the question is different: the offspring could be $YY$ or $Yy$. These are mutually exclusive outcomes for one offspring, so add their probabilities:

This is the sum rule: add the probabilities of alternative outcomes when only one of them can occur in the same fertilisation. The image below uses $A$ and $a$ instead of $Y$ and $y$, but shows the same heterozygote-by-heterozygote reasoning. Its three shaded cells include one $AA$ and two $Aa$ possibilities.

For a closer look at why multiplication applies within a cell and addition applies across suitable cells, read the single-gene examples in Khan Academy’s Probabilities in genetics. The later multi-gene material is beyond today’s cross.

These probabilities describe likelihoods, not a guaranteed batch of four offspring. A $\frac{1}{4}$ probability of $yy$ means that each offspring in this model has a one-in-four chance of that genotype. It does not mean that every four offspring must include exactly one $yy$. Observed ratios can differ from predictions, especially in small groups.

Turning a cross into an HSC prediction

A strong prediction shows enough working that a marker can see where the answer came from. For a question stating that yellow seeds are dominant and the parents are both heterozygous, a compact response would be:

Let $Y$ represent the dominant yellow-seed allele and $y$ the recessive green-seed allele. Both parents are $Yy$, so each can produce $Y$- and $y$-carrying gametes. A Punnett square for $Yy\times Yy$ gives $YY$, $Yy$, $Yy$ and $yy$. The predicted genotype ratio is $1:2:1$; because both $YY$ and $Yy$ produce yellow seeds, the predicted phenotype ratio is $3$ yellow:$1$ green. The probability that an offspring has green seeds is $\frac{1}{4}$, or $25\%$.

Notice the order of the reasoning. Define the alleles and parental genotypes, identify the possible gametes, combine them, and translate genotypes into the phenotype the question asks about. If a question asks specifically for the probability of $Yy$, report $\frac{1}{2}$, not the $\frac{3}{4}$ probability of the yellow phenotype. Keep the requested ratio’s labels and order clear.

Key takeaways

For a monohybrid cross, each parent contributes one allele for the gene being considered. A Punnett square displays their possible combinations; the inheritance pattern then lets you convert genotype predictions into phenotype predictions. Multiply independent parental contributions to find a particular combination, and add mutually exclusive combinations when more than one produces the requested outcome. Treat every ratio as a prediction, not a promise about a small number of offspring.

Next lesson, you’ll work in the other direction: using pedigrees and offspring ratios as evidence to infer an inheritance pattern rather than starting with both parental genotypes known.