Genetics: practice problems with step-by-step solutions

Free Genetics practice problems with diagrams, hints and full worked solutions. New values every time, at three levels: monohybrid crosses, dihybrid crosses, Hardy–Weinberg.

Free practice problemEasy
♂ Tt♀ TtTtTt

Two Tt parents are crossed. T gives round seeds and is dominant over t, which gives wrinkled seeds. Click the cell for an offspring that has round seeds and is homozygous.

Tt × Tt
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What you practise

  1. Easymonohybrid crosses
  2. Mediumdihybrid crosses
  3. HardHardy–Weinberg

Key formulas

Monohybrid cross (Aa × Aa)
genotypes 1 : 2 : 1, phenotypes 3 : 1
Dihybrid cross
phenotypes 9 : 3 : 3 : 1
Hardy–Weinberg
p + q = 1, p² + 2pq + q² = 1
Independent genes
multiply the probabilities

Learn Genetics from scratch

1Genes, alleles and traits

A gene is a piece of DNA that controls a trait, such as flower colour in pea plants. Every plant or animal has two copies of each gene: one from each parent.

A gene can come in different versions, called alleles. For flower colour, A gives purple and a gives white.

The pair of alleles an organism carries is its genotype: AA, Aa or aa. What you can see, such as purple or white, is its phenotype.

  • Homozygous: two equal alleles, AA or aa.
  • Heterozygous: two different alleles, Aa.

One allele is often dominant (capital letter) over the other, which is recessive (small letter). One dominant allele is enough to show the trait. A recessive trait appears only in aa.

So AA and Aa plants are both purple. Only aa plants are white.

Self-check Purple (A) is dominant over white (a). What colour is a plant with genotype Aa?
  1. It depends on which parent gave the A
  2. Light purple, a mix of both
  3. Purple
  4. White

Answer: Purple. With complete dominance one A is enough: Aa looks the same as AA. A mixed colour would mean incomplete dominance, which is not the case here.

2The Punnett square

Each parent passes on one of its two alleles to each offspring, chosen at random. A parent Aa gives A or a, each with a chance of ½.

A Punnett square lists all combinations. The alleles of one parent go along the top, those of the other along the side, and each box is one equally likely offspring.

For the cross Aa × Aa:

AaAaAAAaAaaa
  • Genotypes: 1 AA : 2 Aa : 1 aa.
  • Phenotypes: 3 purple : 1 white. The chance of a purple offspring is ¾ = 0.75; white is ¼ = 0.25.

A probability is the number of boxes with the outcome divided by 4.

Self-check An Aa plant is crossed with an aa plant. What is the probability that an offspring has white flowers (aa)?
  1. 0.25
  2. 0.5
  3. 0.75
  4. 0

Answer: 0.5. The aa parent always gives a, so the offspring is Aa or aa, each in 2 of the 4 boxes: 2/4 = 0.5. 0.25 is the answer for Aa × Aa.

3Two genes and whole populations

With two genes on different chromosomes, the alleles are passed on independently. So you can treat each gene on its own and multiply the probabilities.

For AaBb × AaBb: tall (A_) has a chance of ¾ and round (B_) of ¾. Tall and round together: ¾ · ¾ = 9/16.

Doing this for all four combinations gives the classic 9 : 3 : 3 : 1 ratio of a dihybrid cross.

For a whole population, the Hardy–Weinberg model describes how common each allele and genotype is. Let p be the frequency of A and q the frequency of a:

p + q = 1 p² + 2pq + q² = 1
  • p² is the fraction AA, 2pq the fraction Aa (the carriers), q² the fraction aa.
  • You can see who is aa, so q² is usually given. Then q = √(q²) and p = 1 − q.

The model holds for a large population with random mating and no selection, mutation or migration.

Self-check For the cross AaBb × AaBb, what is the probability that an offspring is aabb?
  1. 1/16
  2. 1/4
  3. 1/8
  4. 9/16

Answer: 1/16. aa has a chance of ¼ and bb also ¼, so aabb is ¼ · ¼ = 1/16. 1/4 counts only one of the genes, and 9/16 is the chance of both dominant traits.

4The method step by step

Crosses:

  1. Write the genotype of each parent and the alleles each one can pass on.
  2. For one gene: draw the 2 × 2 Punnett square and count the boxes with the asked genotype or phenotype.
  3. For two genes: work out each gene on its own, then multiply the probabilities.
  4. Give the probability as a fraction or a decimal between 0 and 1.

Hardy–Weinberg:

  1. The fraction showing the recessive trait is q². Write a percentage as a decimal: 9% = 0.09.
  2. q = √(q²), then p = 1 − q.
  3. Carriers: 2pq. Homozygous dominant: p². Multiply by the population size for a number of individuals.

5A worked example

Follow every step. Try to predict the next one before you open it.

Worked example

Tall (A) is dominant over short (a), and round seeds (B) over wrinkled (b). The genes are on different chromosomes. For the cross AaBb × Aabb, what is the probability P that an offspring is tall with round seeds?

1

Split the genes

The genes are independent, so look at them one at a time. Height: Aa × Aa. Seed shape: Bb × bb.

2

Height: Aa × Aa

AaAaAAAaAaaa

Tall needs at least one A: 3 of the 4 boxes. P(tall) = ¾ = 0.75.

3

Seed shape: Bb × bb

BbbbBbbbBbbb

Round needs at least one B: 2 of the 4 boxes. P(round) = ½ = 0.5.

4

Multiply

P = 0.75 · 0.5 = 0.375
5

Check the answer

As a fraction this is ¾ · ½ = 3/8. The answer lies between 0 and 1, and it is smaller than each separate probability, as it must be for “both at once”.

Answer

P = 0.375 (3/8)

6Common mistakes

  • Mixing up genotype and phenotype. Aa and AA are different genotypes but the same phenotype.
  • Counting Aa as recessive. A recessive trait shows only in aa.
  • Adding the probabilities of two genes instead of multiplying them.
  • In Hardy–Weinberg, using q² as if it were q. Take the square root first.
  • Forgetting the factor 2 in 2pq for the carriers.
  • Using a percentage as a decimal without dividing by 100.
Self-check A recessive condition affects 9% of a population in Hardy–Weinberg equilibrium. What fraction of the population are carriers?
  1. 0.16
  2. 0.21
  3. 0.42
  4. 0.49

Answer: 0.42. q = √0.09 = 0.3 and p = 0.7, so 2pq = 2 · 0.7 · 0.3 = 0.42. 0.21 forgets the 2, 0.49 is p², and 0.16 uses q = 0.09 without the square root.

7How exam questions look

  • Easy: monohybrid crosses. One gene, such as AA × Aa or Aa × Aa; find the chance of a phenotype or of a genotype such as Aa.
  • Medium: dihybrid crosses. Two independent genes, such as AaBb × Aabb; find the chance of a combination of traits.
  • Hard: Hardy–Weinberg. From the fraction with a recessive trait, find the carriers or the number of homozygous dominant individuals.

Example of a hard question: 4% of 5000 people show a recessive trait. q = 0.2, p = 0.8, so 0.64 · 5000 = 3200 people are homozygous dominant.

Learn it step by step in the appLearn it step by step in the app

Worked examples

Example 1Easy
Aa ♀aa ♂Aaaa????

In pea plants, purple flowers (A) are dominant over white (a). A plant with genotype Aa is crossed with a plant with genotype aa. What is the probability P that an offspring has purple flowers?

Aa × aa

Find P

Show hints
  1. Write the gametes of each parent and fill in the Punnett square.
  2. Each of the four boxes is equally likely.
  3. Purple shows with at least one A: AA or Aa.
Show the answer and the step-by-step solution

Mendelian genetics: each parent passes on one allele of each gene, chosen at random. A Punnett square lists every combination of gametes, each equally likely. A dominant allele (capital letter) shows whenever it is present; a recessive one only in the homozygous form. Genes on different chromosomes are inherited independently, so their probabilities multiply.

Punnett square

Aa, Aa, aa, aa

Count

P = 2/4 = 0.5

Answer

P = 0.5
Example 2Medium
♂♀YXD​Xd​XD​

Duchenne muscular dystrophy is X-linked recessive (allele d). A carrier mother, XDXd, has children with an unaffected father, XDY. The mother's gametes run down the side. Click the cell for an unaffected son.

♀ XDXd♂ XDY
  1. 1Xd × Y
  2. 2Xd × XD
  3. 3XD × Y
  4. 4XD × XD
Show hints
  1. A son gets Y from the father, so his only X comes from the mother.
  2. A daughter gets one X from each parent; a carrier has one d allele.
  3. Look in the Y column.
Show the answer and explanation

Punnett square: one parent's gametes run along the top, the other's down the side. Each cell joins the gamete above it with the gamete beside it, and every cell is equally likely. A recessive trait only shows when both alleles are recessive; for an X-linked trait, sons get their only X from the mother.

Fill the square

XdY, XdXD, XDY, XDXD

Find the cell

XD × Y = XDY

Answer

Cell XD × Y → XDY
Example 3Hard
AA?AaAaaap (A)q (a)p (A)q (a)q² = 0.04N = 10000

In a population of 10000 in Hardy–Weinberg equilibrium, 4% show a recessive trait. How many individuals N are expected to be homozygous dominant?

N = 10000q² = 0.04

Find N

Show hints
  1. q² is the frequency of the recessive phenotype.
  2. Find q, then p = 1 − q. Homozygous dominant individuals have frequency p².
  3. p = 0.8.
Show the answer and the step-by-step solution

Hardy–Weinberg: in a large, randomly mating population with no selection, the allele frequencies p (dominant) and q (recessive), p + q = 1, give genotype frequencies p², 2pq and q².

Allele frequencies

q = √0.04 = 0.2
p = 0.8

Homozygous dominant

p² = 0.64
N = 10000·0.64 = 6400

Answer

N = 6400

Questions and answers

What is Genetics?

A gene is a piece of DNA that controls a trait, such as flower colour in pea plants. Every plant or animal has two copies of each gene: one from each parent.

A gene can come in different versions, called alleles. For flower colour, A gives purple and a gives white.

How do I solve Genetics problems step by step?

Mendelian genetics: each parent passes on one allele of each gene, chosen at random. A Punnett square lists every combination of gametes, each equally likely. A dominant allele (capital letter) shows whenever it is present; a recessive one only in the homozygous form. Genes on different chromosomes are inherited independently, so their probabilities multiply.

What do the Genetics exercises cover?
  • Easy: monohybrid crosses
  • Medium: dihybrid crosses
  • Hard: Hardy–Weinberg

Every problem has new values, so you learn the method instead of an answer. Stuck? Open a small hint first, and the full explanation only when you need it.

How practising works

  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Your progress, mistakes and saved problems are kept, so you can review before the exam.

Calculators

Punnett square calculator

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Biology: Genetics and Cell Biology

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Printable worksheet

Genetics worksheet with answers
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