Punnett Squares

Essential Question

How can we predict the traits of offspring?

If you know the genotypes of two parents, you can predict the chances for the genotypes and phenotypes of their offspring. A Punnett square is a tool that shows every way the parents’ alleles can combine. In this lesson, you’ll set up Punnett squares, turn them into probabilities, and use test crosses to find an unknown genotype.

Setting Up a Punnett Square

• Write one parent’s possible gametes across the top
• Write the other parent’s possible gametes down the side
• Fill each box with the two alleles that meet
• Each box is equally likely

A Punnett square predicts the offspring of a cross. Each parent gives one allele in each gamete, so a heterozygous parent (Rr) makes two kinds of gametes, R and r, with equal chances. Write one parent’s gametes across the top and the other’s down the side, then fill each box with the two alleles that meet. In the example, Rr x Rr gives RR, Rr, Rr, and rr. The genotype ratio is 1 RR : 2 Rr : 1 rr. Because R is dominant, the phenotype ratio is 3 round : 1 wrinkled. This lesson covers crosses that follow one gene at a time (monohybrid crosses).

Probability

• Each box in a 2 x 2 square has a probability of 1/4
• Add the boxes that give the same phenotype
• For two separate events, multiply their probabilities
• Probability describes chance, not a guarantee for each offspring

Offspring	Genotype	Boxes	Probability
Wrinkled	rr	1 of 4	1/4
Round	RR or Rr	3 of 4	3/4
Heterozygous	Rr	2 of 4	1/2

Probability is the chance that something happens, written as a fraction from 0 to 1. In the Rr x Rr cross, 1 of the 4 boxes is rr, so each offspring has a probability of 1/4 of having wrinkled seeds. To find the chance of a phenotype, add the boxes that give it: round seeds are RR, Rr, or Rr, which is 3/4. When two separate events both have to happen, multiply: the chance that two offspring are both wrinkled is 1/4 x 1/4 = 1/16. Probabilities predict what is expected over many offspring. Even when the chance is 1/4, a family with four children may have none, one, or several affected children, because each fertilization is a separate chance event.

Test Crosses

• A dominant phenotype can be homozygous (PP) or heterozygous (Pp)
• A test cross crosses the unknown plant with a homozygous recessive plant (pp)
• If all offspring show the dominant trait, the parent is probably PP
• If about half show the recessive trait, the parent is Pp

A purple pea plant could be PP or Pp, because both look purple. A test cross finds out which. Cross the unknown plant with a white plant (pp). If the unknown plant is PP, every offspring gets a P and is purple. If it is Pp, about half the offspring are purple and half are white. Any white offspring shows that the unknown parent carries a p allele. Breeders use test crosses to find out which of their organisms carry a hidden recessive allele.

A Human Trait: Cystic Fibrosis

• Cystic fibrosis is caused by a recessive allele (c)
• A person with genotype cc has cystic fibrosis
• A carrier (Cc) does not have the condition but can pass on the allele
• Two carriers have a 1/4 chance of a child with cystic fibrosis

Cystic fibrosis is a condition that affects the lungs and digestion. It is caused by a recessive allele of a gene on an autosome, so a person has cystic fibrosis only if they inherit the allele from both parents (cc). A carrier has one copy of the allele (Cc). Carriers do not have the condition, but they can pass the allele to their children. When two carriers have a child, the Punnett square shows a 1/4 chance for each child to have cystic fibrosis, 1/2 to be a carrier, and 1/4 to have neither. Each child has the same chances, no matter how many children the parents already have.

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Worked Examples

Try each problem on your own first, then open the solution to check your work.

Example 1: A Monohybrid Cross

Two heterozygous pea plants (Rr), with R = round seeds and r = wrinkled seeds, are crossed. (a) Complete a Punnett square and give the genotype ratio. (b) If the cross produces 200 seeds, about how many are wrinkled? (c) What is the probability that two seeds picked at random are both wrinkled?

Parent 1	Parent 2
Rr (round)	Rr (round)

Show the solution

1. (a) Punnett square: Gametes from each parent: R or r. The boxes are RR, Rr, Rr, and rr, so the genotype ratio is 1 RR : 2 Rr : 1 rr.
2. (b) Wrinkled seeds: Only rr is wrinkled, which is 1/4. 1/4 x 200 = 50 seeds.
3. (c) Two wrinkled seeds: The seeds are separate events, so multiply: 1/4 x 1/4 = 1/16.
4. Answer: (a) 1 RR : 2 Rr : 1 rr. (b) About 50 seeds. (c) 1/16.

Example 2: A Test Cross

A purple pea plant (P = purple, p = white) is crossed with a white plant. The offspring are shown in the table. (a) What is the genotype of the purple parent? (b) What would the results look like if the purple parent were PP?

Offspring phenotype	Number
Purple	26
White	24

Show the solution

1. (a) Use the white parent: The white parent is pp, so every offspring gets a p from it. White offspring (pp) must also get a p from the purple parent, so the purple parent has a p allele. It is purple, so it also has a P: genotype Pp. Check: Pp x pp should give 1/2 purple and 1/2 white. 26 : 24 is close to 1 : 1.
2. (b) If PP: PP x pp gives only Pp offspring, so all 50 would be purple.
3. Answer: (a) Pp. (b) All offspring would be purple.

Example 3: Predict a Human Trait

Two parents are carriers of cystic fibrosis (Cc), where c is the recessive allele. (a) What is the probability that a child has cystic fibrosis? (b) What is the probability that two children both have it? (c) A child of these parents does not have cystic fibrosis. What is the probability that the child is a carrier?

Show the solution

1. (a) One child: Cc x Cc gives CC, Cc, Cc, and cc. Only cc has cystic fibrosis, so the probability is 1/4.
2. (b) Two children: Each child is a separate event, so multiply: 1/4 x 1/4 = 1/16.
3. (c) A child without the condition: We know the child is not cc, so only 3 boxes remain: CC, Cc, and Cc. Two of these 3 are carriers, so the probability is 2/3.
4. Answer: (a) 1/4. (b) 1/16. (c) 2/3.

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Practice

Practice filling in Punnett squares, turning them into probabilities, using a test cross, and predicting the chance of a recessive condition. Try it on your own first, then check your work with the answer key.

• Punnett Squares Practice Worksheet (PDF)
• Punnett Squares Practice Answer Key (PDF)

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Lesson Slides

• 10.5 Punnett Squares Slides (PDF)

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Big Ideas

• A Punnett square shows every way two parents’ alleles can combine
• Each box is equally likely, so boxes become probabilities
• Multiply probabilities for separate events
• A test cross reveals a hidden recessive allele
• Probabilities predict chance, not what will happen in each family

Back to the essential question: A Punnett square predicts offspring because each parent passes on one of its two alleles with equal chance, so each box is equally likely. Adding boxes gives probabilities for genotypes and phenotypes. Next, you’ll see inheritance patterns where one allele is not simply dominant.

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