GAMSAT Genetics: Pedigrees and Probability

Most GAMSAT genetics questions are probability questions in disguise. Two rules, one conditional step and four pedigree tells, worked without a calculator.

2 rules

and → multiply · or → add

1 : 2 : 1

the carrier × carrier cross, by genotype

2/3

an unaffected child of two carriers is a carrier

calculators — keep everything as fractions

Genetics in the sciences paper rarely asks you to recall a fact. It hands you a family tree or a cross, tells you something about how a trait behaves, and asks for a probability. The biology is first-year; the marks are lost in the arithmetic and, more often, in the wording.

So treat a genetics unit as what it mostly is: a probability problem with a biological story attached. Get the story right once, then let two rules and one conditional step do the rest.

Two rules do almost all the work

Product rule

Sum rule

When

Two independent events both happen

One of several mutually exclusive outcomes happens

The word in the question

and · both · first and second

or · either · at least one way

What you do

Multiply the probabilities

Add the probabilities

Example

Two affected children: 1/4 × 1/4 = 1/16

Child is AA or Aa: 1/4 + 1/2 = 3/4

Nearly every genetics probability is these two rules, applied in the right order.

The product rule: the probability that two independent things both happen is the product of their probabilities. The sum rule: the probability that one of several mutually exclusive outcomes happens is the sum of theirs. "And" means multiply; "or" means add. Nearly every genetics probability you will be asked is these two rules applied in the right order.

The crosses to know cold

Aa × Aa

	A	a
A	AA	Aa
a	Aa	aa

Genotypes: 2 Aa : 1 aa : 1 AA

Phenotypes: 3 A_ : 1 aa (assuming complete dominance)

Two carriers of a recessive allele (Aa × Aa) produce AA, Aa and aa in a 1 : 2 : 1 ratio, so a quarter of their children are expected to show the recessive trait and three quarters not. A carrier crossed with an affected parent (Aa × aa) gives a 1 : 1 split. Those two ratios, held as fractions, cover a surprising share of the paper.

Apply the rules, one child at a time

Question	Working	Answer
One child affected	aa from Aa × Aa	1/4
Two children, both affected	1/4 × 1/4	1/16
Two children, neither affected	3/4 × 3/4	9/16
Two children, exactly one affected	2 × (1/4 × 3/4)	3/8

Carrier × carrier, each child independently 1/4 affected. 'Exactly one' can happen two ways, so it is counted twice.

Each child of two carriers has a 1/4 chance of being affected, independently of their siblings. Two affected children: 1/4 × 1/4 = 1/16. Exactly one affected out of two is where people slip, because it can happen two ways — first child affected and second not, or the reverse — so it is 2 × (1/4 × 3/4) = 3/8.

The conditional step most people miss

Unaffected changes the denominator

Of the four equally likely outcomes of Aa × Aa — AA, Aa, aA, aa — being unaffected rules out aa. Three remain, and two of those three carry the allele. So an unaffected child of two carriers is a carrier with probability 2/3, not 1/2. It is the step questions are most often built on, because it is the one that feels like a half.

If two carriers have a child who is known to be unaffected, that child's chance of being a carrier is not 1/2. The affected outcome has been ruled out, so only three of the four equally likely outcomes remain — AA, Aa, aA — and two of those three are carriers. The answer is 2/3. Questions are built on this step because it is the one that feels like it should be a half.

Reading a pedigree: which pattern is it?

Pattern	Signature in a pedigree	Cannot happen
Autosomal recessive	Can skip generations; unaffected parents can have an affected child	Two affected parents with an unaffected child
Autosomal dominant	Every affected child has an affected parent	Two unaffected parents with an affected child
X-linked recessive	Mostly males; passed on through carrier mothers	An affected daughter with an unaffected father
X-linked dominant	An affected father passes it to every daughter	An affected father with an unaffected daughter
Mitochondrial	Passed from an affected mother to all her children	Transmission from an affected father

The signature of each mode of inheritance. Settle the mode before any probability — every later fraction depends on it.

Before any probability, settle the mode of inheritance, because every later fraction depends on it. A stimulus will often tell you; when it does not, the pedigree usually contains one family that decides it. The table above gives the signature of each pattern; the families below are the ones that rule patterns out.

1
Unaffected parents, affected child
Recessive.
2
Affected parents, unaffected child
Dominant.
3
Affected daughter, unaffected father
Not X-linked recessive.
4
Father passes it to a son
Not X-linked at all.

Look for one family that decides it rather than fitting everyone at once. These tells assume every relevant genotype shows the trait unless the stimulus says otherwise.

Look for a decisive family rather than trying to fit every individual at once. Two unaffected parents with an affected child means the trait is recessive. Two affected parents with an unaffected child means it is dominant. An affected daughter with an unaffected father rules out X-linked recessive; transmission from father to son rules out X-linked inheritance altogether. Unless the stimulus says otherwise, these tells assume every carrier of the relevant genotype shows the trait.

A three-generation problem, worked

Filled = affected; centre dot = a known carrier. II-2 is unaffected with unaffected parents and an affected sister; II-3 is stated to be a carrier.

Step	Reasoning	Probability
Mode	Unaffected I-1 and I-2 have affected II-1 → recessive; her father is unaffected → autosomal	—
II-2 is a carrier	Unaffected child of two carriers	2/3
Child affected, given II-2 is a carrier	Aa × Aa	1/4
Child affected	2/3 × 1/4	1/6

Three lines of fractions. The 2/3 is the conditional step; the 1/4 is the carrier cross.

Two unaffected parents have an affected daughter, so the trait is recessive — and because her father is unaffected, it is autosomal, not X-linked. Their unaffected son therefore has a 2/3 chance of being a carrier. If he has children with a known carrier, each child is affected only if he is a carrier and then passes the allele with his partner: 2/3 × 1/4 = 1/6.

Read the question's wording twice

"Their next child is an affected son"

"A son of theirs is affected"

What is unknown

The sex and the genotype

Only the genotype — the sex is given

Working

1/2 (son) × 1/2 (gets the X carrying the allele)

1/2 (gets the X carrying the allele)

Answer

1/4

1/2

Carrier mother × unaffected father, X-linked recessive. Same family, two questions, two answers.

X-linked questions in particular turn on a few words. For a carrier mother and an unaffected father, "the probability that their next child is an affected son" is 1/4, while "the probability that a son of theirs is affected" is 1/2, because the second has already told you the child is a son. Neither number is harder to compute; the marks go to whoever noticed which question was asked.

Keep fractions, not decimals

1/4

affected child of two carriers

2/3

unaffected child of two carriers is a carrier

1/6

2/3 × 1/4 — the classic three-generation answer

3/8

exactly one of two children affected

Without a calculator, fractions are faster and safer than decimals. Multiply numerators and denominators, cancel early, and the answer options — usually written as fractions — line up with what you have. Two-thirds times a quarter is two-twelfths is a sixth; as decimals the same step invites an error. Our post on mental maths for Sciences drills the arithmetic itself.

Use the stimulus's rules, not your textbook's

Twist the stimulus may describe	What changes
Incomplete dominance	Heterozygotes show an intermediate phenotype, so 1 : 2 : 1 is visible as three phenotypes
Codominance	Both alleles are expressed in the heterozygote — again three phenotypes
Linked genes	Alleles on the same chromosome tend to be inherited together, so independent assortment no longer holds
A trait not every carrier shows	An unaffected person can still carry and pass on the relevant genotype — the pedigree tells weaken

The two rules survive every twist; only the ratios you feed them change. Use the stimulus's description of the mechanism.

Sciences assesses the ability to apply knowledge in new contexts, and genetics units often introduce a twist: incomplete dominance, codominance, linked genes, or a trait that not every carrier shows. When the stimulus describes the mechanism, use its description, even where it departs from the simple Mendelian case you learned. The two rules still apply; only the ratios you feed them change.

Where it sits in the paper

questions in the sciences paper

150 min

for all of them

~2 min

each, on average

2×

its weight in ACER's overall

The sciences paper is 75 questions in 150 minutes — about two minutes each — and it counts twice in ACER's overall. A genetics unit you can settle in three lines of fractions is time banked for the questions that genuinely need longer.

Practise it on a real clock

1
Settle the mode
Find the one family that decides it.
2
Write the fractions
Product rule for and, sum rule for or.
3
Check the condition
Unaffected? Already known to be a son?
4
Then time it
Three lines of working, about two minutes.

A method does nothing until it has met a timer.

A method does nothing until it has met a timer. Our free 15-minute practice test runs six questions at exam pace with the reasoning shown after each answer, and the Sciences data pack gives a longer sitting on stimulus-driven science with every step written out.

GAMSAT® is a registered trademark of ACER. ACER is not affiliated with, and does not endorse, Aptavia.

Key takeaways

Most genetics questions are probability questions: and means multiply, or means add.
Know Aa × Aa (1 : 2 : 1, a quarter affected) and Aa × aa (1 : 1) as fractions.
'Exactly one of two' happens two ways — count it twice: 2 × (1/4 × 3/4) = 3/8.
An unaffected child of two carriers is a carrier with probability 2/3, not 1/2.
Settle the mode of inheritance first by finding one decisive family in the pedigree.
An affected daughter with an unaffected father rules out X-linked recessive; father-to-son transmission rules out X-linked altogether.
Read the wording twice: 'an affected son' and 'a son who is affected' are different questions.
Keep fractions, and use the stimulus's mechanism when it departs from the textbook.

Frequently asked questions

Is genetics in GAMSAT Section III?

Genetics is part of the biology the sciences paper draws on, usually as a family tree or a cross with a probability to find. The biology is first-year level; most marks are lost in the arithmetic and the wording rather than in recall.

How do you calculate genetic probabilities without a calculator?

With two rules and fractions. The product rule — for independent events, multiply — and the sum rule — for mutually exclusive outcomes, add. Keep everything as fractions and cancel early: two-thirds times a quarter is a sixth.

Why is the probability 2/3 and not 1/2 that an unaffected child of two carriers is a carrier?

Because being unaffected rules out one of the four equally likely outcomes. Of the three that remain — AA, Aa and aA — two are carriers, so the probability is 2/3. It is the most commonly tested step in pedigree questions.

How do you tell autosomal from X-linked inheritance in a pedigree?

Look for a decisive family. An affected daughter with an unaffected father rules out X-linked recessive, and transmission from father to son rules out X-linked inheritance altogether. Two unaffected parents with an affected child show the trait is recessive; two affected parents with an unaffected child show it is dominant.

What if the GAMSAT stimulus describes a different inheritance pattern from the textbook?

Use the stimulus. Sciences assesses applying knowledge in new contexts, and genetics units often describe incomplete dominance, codominance, linked genes or a trait not every carrier shows. The product and sum rules still apply; only the ratios you feed them change.