Answer key · Unit 7

Inheritance.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Misconception catalogue

Answer key 4

Lesson 1 of 4 · About 20 minutes

Genes and alleles

Two copies of every gene, a dominant allele hiding a recessive one, genotype and phenotype, and why a white flower can come from two purple parents.

Open the lesson

The 4 steps and their answers

Step 1 of 4
Open this step
Two copies
Practice · Choose
Question
Both plants in the Scene have the genotype Pp: one copy of the allele for purple flowers, and one copy of the allele for white. What colour do they flower?

Correct answer
- Correct Purple
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
100default
Cross the parents
Parents
Choices
Shown in a random order.
- Correct Purple
- Wrong Pale purple, halfway
  Misconception: Thinks the offspring of a purple and a white parent come out a blend, pale purple.
  Feedback from the catalogue
  Alleles do not mix like paints. Each allele stays whole, and the dominant one simply covers the recessive one: a Pp plant flowers fully purple, just like PP. The white allele is still there, and can pass to the next generation and show up again in a pp plant. That is what Mendel found: inheritance comes in separate units.
- Wrong White
  Feedback
  P is written as a capital because it is the dominant one: one copy of it is enough to make the flower purple.
- Wrong Purple and white patches
  Misconception: Thinks the offspring of a purple and a white parent come out a blend, pale purple.
  Feedback from the catalogue
  Alleles do not mix like paints. Each allele stays whole, and the dominant one simply covers the recessive one: a Pp plant flowers fully purple, just like PP. The white allele is still there, and can pass to the next generation and show up again in a pp plant. That is what Mendel found: inheritance comes in separate units.
Feedback for a right answer
Purple, just like a PP plant. The dominant allele P covers the recessive allele p, but p does not vanish: the plant carries it and can pass it on.

Hint
Look at the parents’ flowers in the Scene.

Worked solution
1. Each plant has two copies of the gene for flower colour, one from each parent.
2. P is dominant: one copy of it is enough to make the flower purple.
3. So Pp flowers purple, like PP. Only pp, with no P, flowers white.
If you chose pale purple, you thought the alleles mix. In Mendel’s peas they do not.
Step 2 of 4
Open this step
Pure-breeding
Practice · Calculate
Question
Now the seed parent is PP, pure purple, and the pollen parent pp, white. What percentage of the offspring will flower purple?

Correct answer
100 ± 0.5
Setup, choices and feedback
The Scene at this step
Seed parent
PPfixed
Pollen parent
ppfixed
Seedlings
100default
Cross the parents
Parentsfixed
Accepted within
± 0.5
Computed from the Scene at this step’s setting
Share of seedlings the square predicts will flower purple, 0..1/nodes/cross/outputs/expectedPurple
Wrong answers it recognises
- 50 ± 0.5
  Misconception: Thinks the offspring of a purple and a white parent come out a blend, pale purple.
  Feedback
  A half would be right if each offspring took the colour of one parent. But each offspring gets an allele from each parent: P from one and p from the other.
- 75 ± 0.5
  Misconception: Assumes a recessive trait turns up in a quarter of the offspring in every cross.
  Feedback from the catalogue
  A quarter is the answer only when both parents are Pp. Every cross needs its own square: when one parent is pp, every offspring gets p from it, and the half that also get p from the other parent are white, that is a half. And when one parent is PP, no offspring is white.
Feedback for a right answer
$100\%$ ⁠: a PP parent always gives P, and a pp parent always p, so every offspring is Pp, and all are purple. That is how Mendel got his first generation: every flower purple, and the white gone, apparently.

Hint
What can each parent give? Write out the four boxes.

Worked solution
1. The seed parent PP can only give P.
2. The pollen parent pp can only give p.
3. All four boxes are Pp, and all flower purple.
4. The percentage: $\frac44 = 100\%$ ⁠.
Step 3 of 4
Open this step
White comes back
Practice · Predict, then look
Question
Both parents are purple, and both are Pp. Can they have a white offspring?

Correct answer
- Correct Yes, about one in four
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
100default
Cross the parents
Parentsfixed
Choices
- Correct Yes, about one in four
- Wrong No: purple parents have only purple offspring
  Misconception: Thinks a recessive trait that is hidden in the parents cannot appear in their offspring.
  Feedback from the catalogue
  A hidden recessive allele is not lost. A Pp plant carries p and passes it to half its sex cells. When two Pp parents both give p, the offspring is pp, and white. So two purple parents can have a white offspring, with a chance of a quarter. That is also how recessive diseases appear in children of two healthy parents who are carriers.
- Wrong Yes, half of them
  Misconception: Treats the three genotypes PP, Pp and pp as equally likely.
  Feedback from the catalogue
  Three genotypes are not three equal chances. What is equal is the square’s four boxes, and Pp takes two of them. So in a cross of Pp with Pp the chance of a purple flower is $\frac{3}{4}$ ⁠, not $\frac{2}{3}$ ⁠.
Once the prediction is locked in, the Scene changes
Cross the parents
Punnett squarefixed
The Scene then shows: 1 · Boxes of the four that flower white (pp)/nodes/cross/outputs/whiteBoxes
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
One box in four is pp: p from each parent. The white was hidden in both parents, and turned up again in the next generation. That is just what Mendel saw in his second generation: about one white flower for every three purple.

Hint
Each parent passes on one of its two copies. What if both pass on p?

Worked solution
1. Each Pp parent passes on P with chance one half and p with chance one half.
2. In the square: PP, Pp, pP, pp. Each box is a quarter.
3. Only pp is white: one box out of four. After the reveal the square shows one white box.
Step 4 of 4
Open this step
Dominant does not mean common
Practice · Choose
Question
The purple allele is dominant over the white one. What can you conclude from that about a field of wild peas?

Correct answer
- Correct Only that a Pp plant flowers purple. How many purple flowers the field has can’t be told from that
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
100default
Cross the parents
Punnett square
Choices
Shown in a random order.
- Correct Only that a Pp plant flowers purple. How many purple flowers the field has can’t be told from that
- Wrong That most of the field’s flowers are purple
  Misconception: Thinks a dominant allele is the commoner one in a population.
  Feedback from the catalogue
  “Dominant” says only what happens when both alleles are together in one individual: which of them shows. It says nothing about how common the allele is. Extra fingers come from a dominant allele, and are rare. Blood group O is set by a recessive allele, and is the commonest in the world. How common an allele is depends on the population’s history and on natural selection, not on dominance.
- Wrong That the white allele will die out in time
  Misconception: Thinks a dominant allele is the commoner one in a population.
  Feedback from the catalogue
  “Dominant” says only what happens when both alleles are together in one individual: which of them shows. It says nothing about how common the allele is. Extra fingers come from a dominant allele, and are rare. Blood group O is set by a recessive allele, and is the commonest in the world. How common an allele is depends on the population’s history and on natural selection, not on dominance.
Feedback for a right answer
Dominance is a rule about one individual: which allele shows when both are together. A field can be mostly white, if the white allele is common in it. So in people: extra fingers are dominant and rare, and blood group O is recessive and common.

Hint
What exactly does the word “dominant” speak about: one individual, or a population?

Worked solution
1. Dominance decides the phenotype of the heterozygote, Pp.
2. How many purple flowers the field has depends on how many P and p alleles it holds, which is set by the population’s history.
3. So dominance tells you neither how many flowers will be purple, nor that an allele will disappear. Without natural selection, an allele’s share does not change just because it is recessive.

Lesson 2 of 4 · About 25 minutes

Punnett squares

How to build a Punnett square from what each parent can pass on, the 1 : 2 : 1 ratio of genotypes and 3 : 1 of colours, and a test cross that reveals a hidden genotype.

Open the lesson

The 5 steps and their answers

Step 1 of 5
Open this step
Filling the square
Practice · Calculate
Question
In a cross of Pp with Pp, in how many of the four boxes of the Punnett square is the genotype Pp?

Correct answer
2 ± 0.1
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
100default
Cross the parents
Parentsfixed
Accepted within
± 0.1
Computed from the Scene at this step’s setting
Boxes of the four that are Pp/nodes/cross/outputs/heterozygous
Wrong answers it recognises
- 1 ± 0.1
  Misconception: Counts Pp only once in a Pp × Pp square, as if Pp and pP were the same box.
  Feedback from the catalogue
  The square has four boxes, each as likely as the others. Pp appears in two of them: P from the seed parent and p from the pollen, or p from the seed parent and P from the pollen. Those are two different ways to the same genotype, so it is twice as likely as PP or pp: the ratio is $1 : 2 : 1$ ⁠.
- 3 ± 0.1
  Misconception: Counts Pp only once in a Pp × Pp square, as if Pp and pP were the same box.
  Feedback
  $3$ ⁠ is the number of purple boxes: PP and two Pp boxes. The question is only about Pp.
Feedback for a right answer
Two: P from the seed parent and p from the pollen, and p from the seed parent and P from the pollen. The genotypes come in $1 : 2 : 1$ ⁠, and the colours in $3 : 1$ ⁠.

Hint
The square’s rows are the seed parent’s alleles, and its columns the pollen parent’s. Fill each box with a letter from its row and one from its column.

Worked solution
1. Rows: P and p (the seed parent). Columns: P and p (the pollen parent).
2. The boxes: PP, Pp, pP, pp.
3. pP and Pp are the same genotype, and both are written Pp.
4. Pp boxes: $2$ ⁠.
If you answered $1$ ⁠, you counted the two ways of getting Pp as one.
Step 2 of 5
Open this step
From genotypes to colours
Practice · Calculate
Question
In the same cross, Pp with Pp, what is the chance that one seed grows into a plant with purple flowers? Answer as a percentage.

Correct answer
75 ± 0.5
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
100default
Cross the parents
Parentsfixed
Accepted within
± 0.5
Computed from the Scene at this step’s setting
Share of seedlings the square predicts will flower purple, 0..1/nodes/cross/outputs/expectedPurple
Wrong answers it recognises
- 66.67 ± 1
  Misconception: Treats the three genotypes PP, Pp and pp as equally likely.
  Feedback from the catalogue
  Three genotypes are not three equal chances. What is equal is the square’s four boxes, and Pp takes two of them. So in a cross of Pp with Pp the chance of a purple flower is $\frac{3}{4}$ ⁠, not $\frac{2}{3}$ ⁠.
- 50 ± 0.5
  Misconception: Counts Pp only once in a Pp × Pp square, as if Pp and pP were the same box.
  Feedback from the catalogue
  The square has four boxes, each as likely as the others. Pp appears in two of them: P from the seed parent and p from the pollen, or p from the seed parent and P from the pollen. Those are two different ways to the same genotype, so it is twice as likely as PP or pp: the ratio is $1 : 2 : 1$ ⁠.
- 25 ± 0.5
  Misconception: Thinks a recessive trait that is hidden in the parents cannot appear in their offspring.
  Feedback
  $25\%$ ⁠ is the chance of white. The purple ones are the other three boxes.
Feedback for a right answer
$75\%$ ⁠: three boxes of four equally likely ones, PP and two Pp. That is the “purple” part of the $3 : 1$ ⁠ ratio.

Hint
How many boxes have at least one P?

Worked solution
1. The four boxes are equally likely, each $\frac14$ ⁠.
2. Purple ones: PP, Pp, Pp, that is three.
3. The chance: $\frac34 = 75\%$ ⁠.
If you answered about $67\%$ ⁠, you took three equal genotypes, two of them purple. But Pp is worth two boxes.
Step 3 of 5
Open this step
The test cross
Practice · Reach the target
Question
You have a purple plant, and want to know whether it is PP or Pp. The way: a test cross, a cross with a white plant. Seed parent is the Pp plant. Choose Pollen parent so that the square predicts half purple and half white offspring, then press Check.

Goal
- 0.5 ± 0.01
  At the start of the step: 1
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
PP
Seedlings
100default
Cross the parents
Punnett square
Read from the Scene at
Share of seedlings the square predicts will flower purple, 0..1/nodes/cross/outputs/expectedPurple
One setting that reaches it
Pollen parent
pp
Seedlings
4
Feedback for a right answer
Pp with pp: half the offspring Pp and half pp. Had the purple plant been PP, every offspring would be purple. So a single white offspring is enough to know the purple parent is Pp.

Feedback for a wrong answer
Not yet. Which parent always passes on p, so that each offspring’s colour is set by the other parent alone?

Hint
A test cross is always made with a recessive parent, which passes on only p.

Worked solution
1. A pp parent always passes on p.
2. So each offspring’s colour depends only on the allele from the Pp parent: P half the time, p half the time.
3. Choose Pollen parent: pp. The square: Pp, Pp, pp, pp, half purple and half white.
Step 4 of 5
Open this step
All carriers
Practice · Reach the target
Question
Choose both parents so that all four boxes of the square are Pp, then press Check.

Goal
- 4 ± 0.1
  At the start of the step: 2
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
100default
Cross the parents
Punnett square
Read from the Scene at
Boxes of the four that are Pp/nodes/cross/outputs/heterozygous
One setting that reaches it
Seed parent
pp
Pollen parent
PP
Seedlings
4
Feedback for a right answer
PP with pp: every offspring is Pp, purple and carrying white. That is Mendel’s first cross, between two pure-breeding varieties.

Feedback for a wrong answer
Not yet. A Pp parent sometimes passes on P and sometimes p, so other boxes turn up too.

Hint
For every offspring to get exactly one P and one p, one parent must always give P, and the other always p.

Worked solution
1. Every box needs one P and one p.
2. If one parent is PP, all its rows are P. If the other is pp, all its columns are p.
3. Choose Seed parent PP and Pollen parent pp, or the other way round: four Pp boxes.
Step 5 of 5
Open this step
Purple, but which?
Practice · Calculate
Question
A cross of PP with Pp. In how many of the four boxes is the genotype PP?

Correct answer
2 ± 0.1
Setup, choices and feedback
The Scene at this step
Seed parent
PPfixed
Pollen parent
Ppfixed
Seedlings
100default
Cross the parents
Parentsfixed
Accepted within
± 0.1
Computed from the Scene at this step’s setting
Boxes of the four that are PP/nodes/cross/outputs/homozygousDominant
Wrong answers it recognises
- 4 ± 0.1
  Misconception: Thinks the offspring of a purple and a white parent come out a blend, pale purple.
  Feedback
  All four boxes are purple, but not all are PP: half of them got p from the Pp parent.
- 1 ± 0.1
  Misconception: Assumes a recessive trait turns up in a quarter of the offspring in every cross.
  Feedback
  One PP box comes from a cross of Pp with Pp. Here one parent is PP, and always gives P.
Feedback for a right answer
$2$ ⁠ out of $4$ ⁠: the PP parent always gives P, and the Pp parent gives P half the time. Every offspring is purple, half PP and half Pp, and you cannot tell them apart by colour.

Hint
A PP parent always gives P. What does the other parent give?

Worked solution
1. Rows (PP): P and P. Columns (Pp): P and p.
2. The boxes: PP, Pp, PP, Pp.
3. PP boxes: $2$ ⁠.

Lesson 3 of 4 · About 25 minutes

Chance and offspring

The Punnett square as a map of chances: an expected number of offspring, Mendel's counts, why a small sample strays from the ratio, and multiplying the chances of different offspring.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
An expected number
Practice · Calculate
Question
You sow $100$ ⁠ seeds from a cross of Pp with Pp. How many purple seedlings does the square lead you to expect?

Correct answer
75 ± 0.5
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
100fixed
Cross the parents
Punnett square
Accepted within
± 0.5
Computed from the Scene at this step’s setting
Purple seedlings the square predicts among those sown: the share times the seedlings/nodes/cross/outputs/expectedPurpleSeedlings
Wrong answers it recognises
- 50 ± 0.5
  Misconception: Counts Pp only once in a Pp × Pp square, as if Pp and pP were the same box.
  Feedback from the catalogue
  The square has four boxes, each as likely as the others. Pp appears in two of them: P from the seed parent and p from the pollen, or p from the seed parent and P from the pollen. Those are two different ways to the same genotype, so it is twice as likely as PP or pp: the ratio is $1 : 2 : 1$ ⁠.
- 66.67 ± 1
  Misconception: Treats the three genotypes PP, Pp and pp as equally likely.
  Feedback from the catalogue
  Three genotypes are not three equal chances. What is equal is the square’s four boxes, and Pp takes two of them. So in a cross of Pp with Pp the chance of a purple flower is $\frac{3}{4}$ ⁠, not $\frac{2}{3}$ ⁠.
Feedback for a right answer
$\frac34 \times 100 = 75$ ⁠. That is an expected number: a real bed might give $71$ ⁠ or $79$ ⁠, and sometimes further off still.

Hint
The expected number is the probability times the number of seeds.

Worked solution
1. The chance of a purple seedling: $\frac34$ ⁠.
2. The expected number: $\frac34 \times 100 = 75$ ⁠.
3. Expected white: $100 - 75 = 25$ ⁠.
Step 2 of 6
Open this step
Mendel's count
Practice · Calculate
Question
Mendel grew $929$ ⁠ plants from a cross of Pp with Pp. How many of them were expected to flower purple? Round to a whole plant.

Correct answer
696.8 ± 1
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
929fixed
Cross the parents
Punnett square
Accepted within
± 1
Computed from the Scene at this step’s setting
Purple seedlings the square predicts among those sown: the share times the seedlings/nodes/cross/outputs/expectedPurpleSeedlings
Wrong answers it recognises
- 619.3 ± 1.5
  Misconception: Treats the three genotypes PP, Pp and pp as equally likely.
  Feedback from the catalogue
  Three genotypes are not three equal chances. What is equal is the square’s four boxes, and Pp takes two of them. So in a cross of Pp with Pp the chance of a purple flower is $\frac{3}{4}$ ⁠, not $\frac{2}{3}$ ⁠.
- 464.5 ± 1
  Misconception: Counts Pp only once in a Pp × Pp square, as if Pp and pP were the same box.
  Feedback from the catalogue
  The square has four boxes, each as likely as the others. Pp appears in two of them: P from the seed parent and p from the pollen, or p from the seed parent and P from the pollen. Those are two different ways to the same genotype, so it is twice as likely as PP or pp: the ratio is $1 : 2 : 1$ ⁠.
Feedback for a right answer
$\frac34 \times 929 \approx 697$ ⁠. Mendel counted $705$ ⁠ purple and $224$ ⁠ white: a ratio of $3.15 : 1$ ⁠, very close to $3 : 1$ ⁠.

Hint
$\frac34$ ⁠ of $929$ ⁠.

Worked solution
1. The chance of purple: $\frac34$ ⁠.
2. $\frac34 \times 929 = 696.75$ ⁠.
3. About $697$ ⁠ purple plants, and $232$ ⁠ white.
Mendel got $705$ ⁠: $8$ ⁠ more than expected, a perfectly ordinary difference for a sample this size.
Step 3 of 6
Open this step
Small samples
Practice · Predict, then look
Question
You sow only $4$ ⁠ seeds from a cross of Pp with Pp. How many of the seedlings will flower purple?

Correct answer
- Correct Most likely $3$ ⁠, but any number from $0$ ⁠ to $4$ ⁠ is possible
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
Ppfixed
Seedlings
4fixed
Cross the parents
Punnett squarefixed
Choices
- Correct Most likely $3$ ⁠, but any number from $0$ ⁠ to $4$ ⁠ is possible
- Wrong Exactly $3$ ⁠, always: that’s the $3 : 1$ ⁠ ratio
  Misconception: Thinks a 3 : 1 ratio means every four seedlings hold exactly three purple and one white.
  Feedback from the catalogue
  The $3 : 1$ ⁠ ratio is a probability, not a promise. Each seedling is a separate draw, so four seedlings can come out $4$ ⁠ purple, $2$ ⁠, or even none. Only with many seedlings does the purple share come close to $75\%$ ⁠, just as a coin tossed many times comes close to half heads.
- Wrong All $4$ ⁠, because both parents are purple
  Misconception: Thinks a recessive trait that is hidden in the parents cannot appear in their offspring.
  Feedback from the catalogue
  A hidden recessive allele is not lost. A Pp plant carries p and passes it to half its sex cells. When two Pp parents both give p, the offspring is pp, and white. So two purple parents can have a white offspring, with a chance of a quarter. That is also how recessive diseases appear in children of two healthy parents who are carriers.
Once the prediction is locked in, the Scene changes
Cross the parents
Seedlings countedfixed
The Scene then shows: 3 · Purple seedlings the square predicts among those sown: the share times the seedlings/nodes/cross/outputs/expectedPurpleSeedlings
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The expected average is $3$ ⁠, but in a bed of four the chance of getting exactly $3$ ⁠ is only about $42\%$ ⁠. Watch the bed while the Scene plays, and you will see it re-sown and changing each time.

Hint
Each seedling is a separate draw. Must four draws split by the ratio?

Worked solution
1. Each seedling is purple with chance $\frac34$ ⁠, independently of the others.
2. The expected number: $4 \times \frac34 = 3$ ⁠.
3. The chance of exactly $3$ ⁠: $4 \times \left(\frac34\right)^3 \times \frac14 \approx 0.42$ ⁠.
4. The chance of all $4$ ⁠: $\left(\frac34\right)^4 \approx 0.32$ ⁠, and there is a small chance of $2$ ⁠, $1$ ⁠ or $0$ ⁠ too.
A ratio is what the shares approach when there are many offspring, not what happens in every small group.
Step 4 of 6
Open this step
No memory
Practice · Choose
Question
From a cross of Pp with Pp three seeds have already come up, and all three are purple. What is the chance that the fourth seedling is white?

Correct answer
- Correct $\frac14$ ⁠, like any other seedling
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
4
Cross the parents
Seedlings counted
Choices
Shown in a random order.
- Correct $\frac14$ ⁠, like any other seedling
- Wrong Almost certain: white is due
  Misconception: Thinks earlier offspring change the chances for the next one, so a white must be "due".
  Feedback from the catalogue
  Seedlings have no memory. Each seed comes from a fresh draw of an allele from each parent, so the chance of a white seedling is a quarter, however many purple came before. That is true in families too: if two carrier parents already have three healthy children, the chance that the fourth is affected is still a quarter.
- Wrong Zero: the parents must be PP
  Feedback
  The parents are known to be Pp. Three purple in a row happens with chance $\left(\frac34\right)^3 \approx 42\%$ ⁠, so it is no surprise at all.
Feedback for a right answer
$\frac14$ ⁠. Each seed comes from a fresh draw of an allele from each parent, and the first three seeds do not change it.

Hint
Does the fourth seed know what came of the first three?

Worked solution
1. Each seed comes from one egg and one pollen grain, each carrying P or p with chance one half.
2. The draws for different seeds are independent.
3. So the chance of white is $\frac12 \times \frac12 = \frac14$ ⁠, whatever came before.
Step 5 of 6
Open this step
Both at once
Practice · Calculate
Question
You pick two seeds at random from a cross of Pp with Pp. What is the chance that both grow into white plants? Answer as a percentage.

Correct answer
6.25 ± 0.1
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
100
Cross the parents
Punnett square
Accepted within
± 0.1
A fixed value in the question
Wrong answers it recognises
- 50 ± 0.1
  Misconception: Adds the chances of two independent events that must both happen, instead of multiplying them.
  Feedback from the catalogue
  When two independent things must both happen, multiply the chances: $\frac14 \times \frac14 = \frac{1}{16}$ ⁠. Adding fits “this or that”, and even then only when they cannot happen together. A quick check: the chance of two things happening together cannot be bigger than the chance of either one.
- 25 ± 0.1
  Misconception: Adds the chances of two independent events that must both happen, instead of multiplying them.
  Feedback
  $25\%$ ⁠ is the chance of one white seed. Two white seeds must both happen, which is less likely.
Feedback for a right answer
$\frac14 \times \frac14 = \frac{1}{16} = 6.25\%$ ⁠. The same sum gives the chance that a carrier couple has two children with a recessive disease.

Hint
Two independent events that must both happen: multiply.

Worked solution
1. The chance one seed is white: $\frac14$ ⁠.
2. The seeds are independent, so the chance both are white: $\frac14 \times \frac14 = \frac{1}{16}$ ⁠.
3. As a percentage: $\frac{1}{16} = 6.25\%$ ⁠.
If you answered $50\%$ ⁠, you added $25\% + 25\%$ ⁠. Adding fits “or”, not “and”.
Step 6 of 6
Open this step
Another cross
Practice · Calculate
Question
Now you sow $200$ ⁠ seeds from a test cross, Pp with pp. How many white seedlings do you expect?

Correct answer
100 ± 0.5
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
ppfixed
Seedlings
200fixed
Cross the parents
Punnett square
Accepted within
± 0.5
Computed from the Scene at this step’s setting
White seedlings the square predicts among those sown/nodes/cross/outputs/expectedWhiteSeedlings
Wrong answers it recognises
- 50 ± 0.5
  Misconception: Assumes a recessive trait turns up in a quarter of the offspring in every cross.
  Feedback from the catalogue
  A quarter is the answer only when both parents are Pp. Every cross needs its own square: when one parent is pp, every offspring gets p from it, and the half that also get p from the other parent are white, that is a half. And when one parent is PP, no offspring is white.
- 150 ± 0.5
  Misconception: Assumes a recessive trait turns up in a quarter of the offspring in every cross.
  Feedback
  $150$ ⁠ is three quarters. That would be the number of purple in a cross of Pp with Pp. This cross needs a square of its own.
Feedback for a right answer
$\frac24 \times 200 = 100$ ⁠: in a test cross half the offspring are white, not a quarter.

Hint
Build the square for Pp with pp. How many white boxes does it have?

Worked solution
1. The square for Pp with pp: Pp, Pp, pp, pp.
2. White boxes: $2$ ⁠ of $4$ ⁠, that is $\frac12$ ⁠.
3. Expected: $\frac12 \times 200 = 100$ ⁠ white seedlings.
If you answered $50$ ⁠, you used the quarter from Pp with Pp. Every cross needs its own square.

Lesson 4 of 4 · About 25 minutes

Sex-linked traits

Genes on the X chromosome: why colour blindness is common in men, how a carrier mother passes it to half her sons, and why the daughters of the same parents are carriers, not colour-blind.

Open the lesson

The 5 steps and their answers

Step 1 of 5
Open this step
X and Y
Practice · Choose
Question
A woman has two X chromosomes, and a man one X and one Y. From whom does a son get his X chromosome?

Correct answer
- Correct Always from his mother
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
Pp
Seedlings
100default
Cross the parents
Parents
Choices
Shown in a random order.
- Correct Always from his mother
- Wrong Always from his father
  Misconception: Thinks a son gets his X chromosome from his father.
  Feedback from the catalogue
  A son gets the Y chromosome from his father, because that is what makes him a son. His X always comes from his mother. So a trait whose gene is on the X passes to sons only from the mother, and a father cannot pass it to his son.
- Wrong From his mother or his father, with equal chance
  Misconception: Thinks a son gets his X chromosome from his father.
  Feedback from the catalogue
  A son gets the Y chromosome from his father, because that is what makes him a son. His X always comes from his mother. So a trait whose gene is on the X passes to sons only from the mother, and a father cannot pass it to his son.
Feedback for a right answer
The father gives a son the Y, so the X must come from the mother. To a daughter the father gives his X, and the mother a second X.

Hint
What exactly did the son get from his father that makes him a son?

Worked solution
1. Every child gets one sex chromosome from each parent.
2. From the mother always an X, since she has no other.
3. From the father X or Y, and that decides: X for a daughter, Y for a son.
4. So a son’s X always came from his mother.
Step 2 of 5
Open this step
A model of the sons
Practice · Reach the target
Question
The bed will now model the sons of a mother who carries colour blindness. Seed parent, Pp, is the mother: P is an X with normal vision, and p an X with the colour-blindness allele. The father gives a son a Y, which has no copy of the gene at all, so it hides nothing. Choose the Pollen parent that behaves like that Y, then press Check.

Goal
- 0.5 ± 0.01
  At the start of the step: 1
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
PP
Seedlings
100default
Cross the parents
Punnett square
Read from the Scene at
Share of seedlings the square predicts will flower purple, 0..1/nodes/cross/outputs/expectedPurple
One setting that reaches it
Pollen parent
pp
Seedlings
4
Feedback for a right answer
pp: it passes on only p, which hides nothing that came from the mother. So each seedling shows the mother’s allele alone, just like a son, who has only one X.

Feedback for a wrong answer
Not yet. If the other parent passes on P, it hides the mother’s allele, and a son gets no copy from his father that could hide it.

Hint
Which parent never covers the allele that came from the mother?

Worked solution
1. A son has one X, from his mother. His Y has no copy of this gene.
2. So the son’s phenotype is set by the mother’s allele alone.
3. In the bed, a pp parent passes on only p, which covers nothing: the seedling’s colour depends only on the seed parent’s allele.
4. Choose Pollen parent: pp.
This is a model, not a real plant: peas do not carry the gene on a sex chromosome. But the arithmetic is the same.
Step 3 of 5
Open this step
Colour-blind sons
Practice · Calculate
Question
In the model of the sons, out of $100$ ⁠ sons of a carrier mother, how many are expected to be colour-blind? (A white seedling is a colour-blind son.)

Correct answer
50 ± 0.5
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
ppfixed
Seedlings
100fixed
Cross the parents
Seedlings counted
Accepted within
± 0.5
Computed from the Scene at this step’s setting
White seedlings the square predicts among those sown/nodes/cross/outputs/expectedWhiteSeedlings
Wrong answers it recognises
- 25 ± 0.5
  Misconception: Assumes a recessive trait turns up in a quarter of the offspring in every cross.
  Feedback from the catalogue
  A quarter is the answer only when both parents are Pp. Every cross needs its own square: when one parent is pp, every offspring gets p from it, and the half that also get p from the other parent are white, that is a half. And when one parent is PP, no offspring is white.
- 0 ± 0.5
  Misconception: Thinks someone who does not show a recessive trait cannot be carrying its allele.
  Feedback
  The mother sees colours normally, but she carries the allele, and passes it to half her sons.
Feedback for a right answer
$50$ ⁠: half the sons get the X with the allele, and have no second X to hide it. That is why colour blindness is so common in men: about $8\%$ ⁠ of men, and under $1\%$ ⁠ of women.

Hint
Each son gets one of the mother’s two X’s, with equal chance.

Worked solution
1. The mother carries one normal X and one X with the allele.
2. Each son gets one of them with chance one half, and a Y from his father.
3. A son who got the X with the allele is colour-blind: he has no second copy.
4. Out of $100$ ⁠ sons: $\frac12 \times 100 = 50$ ⁠.
Step 4 of 5
Open this step
The daughters
Practice · Calculate
Question
Now the bed models the daughters of the same parents: the father sees colours normally and gives every daughter his normal X, like a PP parent. In how many of the four boxes is the daughter a carrier, Pp?

Correct answer
2 ± 0.1
Setup, choices and feedback
The Scene at this step
Seed parent
Ppfixed
Pollen parent
PPfixed
Seedlings
100
Cross the parents
Punnett square
Accepted within
± 0.1
Computed from the Scene at this step’s setting
Boxes of the four that are Pp/nodes/cross/outputs/heterozygous
Wrong answers it recognises
- 0 ± 0.1
  Misconception: Thinks someone who does not show a recessive trait cannot be carrying its allele.
  Feedback from the catalogue
  Someone who does not show a recessive trait may well carry its allele, hidden behind a dominant one. A daughter of a carrier mother and a father with normal vision sees colours normally, but with a chance of a half she is a carrier, and later half her sons will be colour-blind.
- 4 ± 0.1
  Misconception: Thinks someone who does not show a recessive trait cannot be carrying its allele.
  Feedback
  All the daughters see colours normally, but only half got the X with the allele from their mother. The other half are PP.
Feedback for a right answer
Two of four: half the daughters are carriers. No daughter is colour-blind, because the father’s X hides the allele. But the carriers will pass it to half their sons, which is why the trait “skips” through daughters to grandsons.

Hint
The father always gives P. What does the mother give?

Worked solution
1. The father gives every daughter a normal X, P.
2. The mother gives P or p, each with chance one half.
3. The boxes: PP, PP, Pp, Pp.
4. Carriers: $2$ ⁠ of $4$ ⁠, and none colour-blind.
Step 5 of 5
Open this step
Any child
Practice · Calculate
Question
A carrier mother and a father with normal vision have a child. Nobody knows yet whether it is a boy or a girl. What is the chance that it is a colour-blind son? Answer as a percentage.

Correct answer
25 ± 0.1
Setup, choices and feedback
The Scene at this step
Seed parent
Pp
Pollen parent
PP
Seedlings
100
Cross the parents
Punnett square
Accepted within
± 0.1
A fixed value in the question
Wrong answers it recognises
- 50 ± 0.1
  Misconception: Gives the share of sons who are affected as if it were the share of all the children.
  Feedback from the catalogue
  “Half the sons” and “half the children” are not the same. For a child to be a colour-blind son, two things must happen: that it is a son, with a chance of a half, and that it gets the X with the allele from its mother, also with a chance of a half. Together: $\frac12 \times \frac12 = \frac14$ ⁠ of all the children.
- 0 ± 0.1
  Misconception: Thinks someone who does not show a recessive trait cannot be carrying its allele.
  Feedback from the catalogue
  Someone who does not show a recessive trait may well carry its allele, hidden behind a dominant one. A daughter of a carrier mother and a father with normal vision sees colours normally, but with a chance of a half she is a carrier, and later half her sons will be colour-blind.
Feedback for a right answer
$\frac12 \times \frac12 = \frac14 = 25\%$ ⁠: half the children are sons, and half the sons are colour-blind.

Hint
Two things must happen: that it is a son, and that he got the X with the allele.

Worked solution
1. The chance the child is a son: $\frac12$ ⁠.
2. The chance such a son got the X with the allele: $\frac12$ ⁠.
3. The two are independent: $\frac12 \times \frac12 = \frac14$ ⁠.
4. As a percentage: $25\%$ ⁠.
If you answered $50\%$ ⁠, you gave the share of the sons. The question is about all the children.

Across the unit · 12 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

Index

Genes and alleles

Two copies

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

Pure-breeding

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

White comes back

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Hint

Worked solution

Dominant does not mean common

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

Punnett squares

Filling the square

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

From genotypes to colours

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

The test cross

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

All carriers

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

Purple, but which?

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Chance and offspring

An expected number

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Mendel's count

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint