Test inheritance patterns with crosses and probability

Ontario Grade 11 Biology

Genetic Processes

Using simple genetic models to predict possible offspring outcomes

In SNC2D, you learned that cells are the basic units of living things and that scientific models help us study questions. In this lesson, a genetic cross is a model for asking how inherited forms of a trait may appear among offspring. For example, if two plants with purple flowers produce some white-flowered offspring, what could a simple inheritance model predict? A Punnett square organizes the possible allele combinations. Probability describes how likely each outcome is. These tools test whether a proposed pattern fits; they do not guarantee the result for any one offspring.

What you will learn

Define alleles, genotype, phenotype, and a genetic cross.
Use a Punnett square to predict possible offspring genotypes and phenotypes.
Apply probability to calculate expected outcomes without treating them as certain.
Use cross results to assess whether an inheritance pattern fits a simple model.

From a biological question to a model

A trait is a feature that can be observed, such as flower colour. An allele is one version of an inherited form of a trait. For a simple model, imagine one gene with two alleles:

P

for purple flowers and

p

for white flowers. This letter choice is a label in the model, not an explanation of how the trait works inside a cell.

An organism’s genotype is the allele combination used to describe its inherited forms for a trait. In this model, the possible genotypes are

PP

,

Pp

, and

pp

. Its phenotype is the observable form of the trait. We will use a simple dominance model: an organism with at least one

P

allele has purple flowers, while an organism with

pp

has white flowers. A dominant allele is the one expressed in the phenotype when paired with the other allele in this model. A recessive phenotype appears only when both alleles are recessive.

A cross is a model of reproduction between two parents. Each parent contributes one allele for the trait to an offspring. A Punnett square lists the combinations that could result. It predicts possible outcomes and their probabilities, not the exact outcome of a particular offspring.

Pp\rightarrow\text{purple phenotype}

Genotype means allele combination; phenotype means observable trait form.
The simple dominance rule applies only if the observations fit that model.
A prediction is not a guarantee for an individual offspring.

Build and read a Punnett square

To make a Punnett square, write the possible allele contributions from one parent across the top and those from the other parent down the side. Fill each box by combining one allele from each parent. Each box represents one possible allele combination under the model.

For example, if both parents have genotype

Pp

, each can contribute either

P

or

p

. The four boxes contain

PP

,

Pp

,

Pp

, and

pp

. Three of the four combinations predict purple flowers, and one predicts white flowers.

Probability is a way to describe how likely an outcome is. For equally likely boxes, divide the number of boxes with the outcome by the total number of boxes. Thus this cross predicts a

3/4

probability of purple and a

1/4

probability of white for each offspring. Across many offspring, the actual numbers may differ from these expected proportions.

\text{probability} = \frac{\text{matching outcomes}}{\text{total outcomes}}

One allele from each parent forms an offspring genotype.
Count matching boxes to find an outcome’s probability.
A probability describes likelihood, not a promised family result.

Use crosses to test an inheritance pattern

A proposed inheritance pattern is an explanation that can be checked against cross outcomes. First state the model and its assumptions. Then use the parents’ known or proposed genotypes to predict offspring outcomes. Finally, compare those predictions with observations.

Suppose a purple-flowered parent has an unknown genotype. In this model it could be

PP

or

Pp

. Cross it with a white-flowered parent, whose genotype must be

pp

under the stated rules. If the unknown parent is

PP

, all predicted offspring are purple. If it is

Pp

, the model predicts half purple and half white.

Seeing white offspring would rule out the

PP

possibility within this simple model, because that cross cannot produce

pp

. It would support the

Pp

explanation. But not seeing white offspring in a small group does not prove the parent is

PP

: a

Pp

cross can produce purple offspring by chance. More observations may make a comparison more informative, but they do not turn probability into certainty.

Pp\times pp\rightarrow\frac{1}{2}Pp+\frac{1}{2}pp

A test cross compares predictions from possible parent genotypes.
An observation can rule out a model outcome that the cross cannot produce.
A small sample may not match the predicted proportion exactly.

Combine probabilities carefully

For separate offspring in the same simple cross, the probability of an outcome is the same each time under the model. Outcomes from earlier offspring do not make a particular genotype certain for the next one. For example, a white offspring from two

Pp

parents does not mean the next offspring must be purple.

A probability question may ask for a particular sequence of outcomes. When outcomes are treated as independent in the model, multiply their probabilities. For two white offspring from a

Pp

by

Pp

cross, each white outcome has probability

1/4

, so the probability of white followed by white is

1/16

.

Use this method only for the stated model and question. It tests expected inheritance outcomes; it does not describe every possible biological influence on a trait. Keep the conclusion proportional to the evidence: say that results fit, support, or do not fit the simple model, rather than claiming that a small set proves a universal rule.

\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}

Each offspring outcome remains a chance, not a certainty.
For a specified sequence of independent outcomes, multiply the probabilities.
State conclusions as a comparison with the model.

Worked example

Predicting outcomes from two heterozygous parents

In the flower-colour model, purple (

P

) is dominant to white (

p

). Predict the genotype and phenotype probabilities for a cross between two purple plants with genotype

Pp

.

List allele contributions
Each parent has one $P$ and one $p$ allele, so either allele is a possible contribution from that parent.
$P,\ p$
Combine the alleles
Pair one contribution from each parent. The four equally likely combinations are $PP$ , $Pp$ , $Pp$ , and $pp$ . PP,\ Pp,\ Pp,\ pp
Count the outcomes
There is one $PP$ , two $Pp$ , and one $pp$ combination. Under the stated dominance rule, the first three predict purple and the last predicts white.
$\frac{1}{4}PP,\ \frac{1}{2}Pp,\ \frac{1}{4}pp$

Answer: The predicted genotype probabilities are

1/4

PP

,

1/2

Pp

, and

1/4

pp

. The predicted phenotype probabilities are

3/4

purple and

1/4

white.

Check: The genotype probabilities add to 1, and the phenotype probabilities also add to 1. These are predictions for each offspring, not a guaranteed ratio in a small group.

Worked example

Testing an unknown purple genotype

A purple plant with unknown genotype is crossed with a white plant. In the model, what does observing white offspring tell you about the purple parent’s genotype?

Identify the white parent
A white phenotype requires genotype $pp$ under the stated model, so the white parent can contribute only $p$ .
$pp$
Compare the possible purple genotypes
If the purple parent were $PP$ , every offspring would receive $P$ from that parent and $p$ from the white parent. None would be $pp$ . If the purple parent were $Pp$ , it could contribute $p$ , allowing a $pp$ offspring.
$PP\times pp\rightarrow Pp$
Interpret the observation
A white offspring has genotype $pp$ . Its presence rules out $PP$ for the purple parent within this model and supports $Pp$ .
$pp\Rightarrow\text{purple parent }Pp$

Answer: Within the simple model, observing a white offspring supports the conclusion that the purple parent is

Pp

. The observation does not establish a rule beyond the model’s assumptions.

Check: A

Pp

parent crossed with

pp

predicts half purple and half white offspring. That prediction is a probability, not a requirement for every small group.

Worked example

Probability of two white offspring

Two

Pp

plants are crossed. What is the probability that two specified offspring are both white?

Find the chance for one offspring
The cross has one white genotype, $pp$ , among four equally likely combinations. The chance of white for one offspring is $1/4$ .
$P(\text{white})=\frac{1}{4}$
Combine the two chances
For this model, the two specified offspring outcomes are treated as independent. Multiply the chance of white for the first by the chance for the second.
$\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}$

Answer: The probability that both specified offspring are white is

1/16

.

Check: The result is a chance for the two-offspring sequence. It does not mean that one white offspring makes another white offspring more or less likely.

Common mistakes and how to avoid them

Treating a dominant allele as more common or as certain to appear in every offspring.

Correction: Dominant describes the phenotype rule in the model. It does not set how common an allele is or guarantee an offspring’s genotype.

Saying that a CAD 3:1 prediction means exactly three purple offspring for every one white offspring.

Correction: The ratio describes expected probabilities for the model. The outcomes in a small group can differ.

Using phenotype alone to claim that a purple plant must be

PP

.

Correction: Under this model, both

PP

and

Pp

are purple. A suitable cross can help distinguish the possibilities.

Changing the probability for the next offspring because of earlier outcomes.

Correction: For each offspring, use the same cross probabilities under the model. Earlier outcomes do not make a particular next outcome certain.

Lesson summary

A genetic cross models allele contributions from two parents.
Punnett squares list possible genotypes; counting boxes gives probabilities.
Compare predictions with observations to test whether a simple inheritance model fits.
Probabilities describe likelihoods, not certain outcomes for individuals.

Check your understanding

Question 1

In a

Pp

by

Pp

cross, what is the probability of a white-flowered offspring under the stated model?

$1/4$
$1/2$
$3/4$
1

Show answer and explanation

1/4

Only the

pp

combination predicts white. It occurs in one of the four equally likely combinations.

Question 2

A white offspring appears in a cross between a white plant and a purple plant of unknown genotype. Which conclusion fits the model?

The purple parent must be $PP$ .
The purple parent is supported as $Pp$ .
The white parent must be $Pp$ .
The cross proves that every later offspring will be white.

Show answer and explanation

The purple parent is supported as

Pp

.

A white offspring is

pp

. The white parent contributes

p

, so the purple parent must also have contributed

p

. This supports

Pp

within the model.

Question 3

If the probability of white is

1/4

for each offspring, what is the probability that two specified offspring are both white?

$1/8$
$1/16$
$1/4$
$1/2$

Show answer and explanation

1/16

Multiply the two probabilities for the specified independent outcomes:

1/4

times

1/4

equals

1/16

.

Key terms

Allele: One version of an inherited form of a trait.
Genotype: The allele combination used to describe an organism for a trait.
Phenotype: The observable form of a trait.
Dominant allele: In a simple model, an allele whose associated phenotype appears when it is paired with a different allele.
Recessive phenotype: In this simple model, a phenotype that appears when both alleles are recessive.
Punnett square: A grid used to list possible allele combinations in a cross.
Probability: A numerical description of how likely an outcome is.
Cross: A model of reproduction between two parents used to predict possible inherited outcomes.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Biology (SBI3U), expectation D2.4. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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D2.4 · Test inheritance patterns with crosses and probability

Ontario Grade 11 Biology

Using simple genetic models to predict possible offspring outcomes

What you will learn

From a biological question to a model

Build and read a Punnett square

Use crosses to test an inheritance pattern

Combine probabilities carefully

Predicting outcomes from two heterozygous parents

Testing an unknown purple genotype

Probability of two white offspring

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SBI3U

About this lesson and its review